In the PHB it says that hiding takes no action and usually is performed as part of a move action. However if I'm playing a rogue/ranger or rogue/shadowdancer and I have the hide in plain sight ability what are the limitations as to what that can be combined with? For example if I'm mid-battle with shadows within 10 ft. can I hide and then full attack dealing sneak attack damage? Or would hiding be a move action and I would only be able to attack once? If I am able to full attack after hiding would I have to hide after each attack or would one in the beginning be sufficient?
No, you don't need to spend a move action to hide, and you can hide as part of a full attack.
First. The rules say movement is the usual method of activation:
Usually none. Normally, you make a Hide check as part of movement
But that's not a necessity. That's because we also have the following rule:
Your Hide check is opposed by the Spot check of anyone who might see you. You can move up to one-half your normal speed and hide at no penalty. When moving at a speed greater than one-half but less than your normal speed, you take a -5 penalty. It’s practically impossible (-20 penalty) to hide while attacking, running or charging.
So, hide while attacking all you want, you just take a teensy tiny -20 penalty on your check.
As for Hide in Plain Sight and actions, all HiPS does is change the conditions under which you can hide. While Supernatural abilities are activated as a standard action unless otherwise noted (and HiPS is a Supernatural ability), HiPS is generally understood to be a "passive" modification to the character's abilities, not requiring specific activation. I'd compare it to the Paladin's Divine Grace when it comes to this.
TL;DR version: HiPS inherits the actions from normal hiding, and hiding can be done as part of the action of attacking.
Hiding Is Only Accomplished As Part Of Another Action
There are rules for hiding while moving, and rules for hiding while attacking, and in both cases the hiding takes place simultaneously to the other action. Whether that means that you hide before you attack when you take both actions seems to be a matter left to DM. I would personally rule that the order is chosen by the player, so you could certainly move while attacking.
Hide In Plain Sight is a Supernatural Ability, but not a standard action
Remember that Supernatural Abilities only require a standard action "unless otherwise noted." (SRD: Special Abilities). Since Hide In Plain Sight simply modifies the ways you can use the Hide skill, you would use the same action economy as you would normally with that skill.
"Unable To React"
The SRD for 3.5 only says a character is denied their Dexterity bonus to AC if they "cant react to a blow." (SRD: Armor Class). Now nowhere in the SRD or PHB does it seem to say whether you can react or not attacks from hidden characters, but as a DM the RAI answers to me seems obvious; if the target cannot see you and therefore cannot target you, he certainly cannot react to your attacks. This holds true for invisible characters, and even invisible characters have to roll Hide checks: "If you are invisible, you gain a +40 bonus on Hide checks if you are immobile, or a +20 bonus on Hide checks if you’re moving." (SRD: Hide).
But as the line on sniping seems to imply, attacking can blow your cover. You can hide while attacking, attack once with Sneak Attack damage, then use a move action to attempt to hide again, as per the rules for sniping (which in the case of the Shadowdancer or Ranger I'd rule also applies to melee attacks also). If you Full Attack, I'd rule the Sneak Attack only applies to the first attack, though.
Here's How to Hide in Dungeons and Dragons 3.5, but to address specifics, here are
Questions & Answers
Question: With what actions can the supernatural ability hide in plain sight be combined?
Answer: The supernatural ability hide in plain sight isn't, itself, an action and instead changes how the the Hide skill works for the creature that possesses it. As such, anything that can be done while hiding (e.g. attacking, charging, moving, running, sniping, etc.) can be done by a creature possessing the supernatural ability hide in plain sight. (It even might function while the character's sleeping.)
Unlike the ranger's extraordinary ability hide in plain sight, which says simply
While in any sort of natural terrain, a ranger of 17th level or higher can use the Hide skill even while being observed.
the assassin's and shadowdancer's supernatural ability hide in plain sight says that a creature
can use the Hide skill even while being observed. As long as she is within 10 feet of some sort of shadow, [the creature] can hide herself from view in the open without anything to actually hide behind. She cannot, however, hide in her own shadow.
The extraordinary ability hide in plain sight only eliminates one of the major issues with hiding--the inability to hide while being observed--, but it doesn't eliminate the other--needing concealment or cover to hide.
But the supernatural ability hide in plain sight eliminates both the major issues with hiding--the inability to hide while being observed and (if within 10 ft. of a shadow the creature who possesses the ability's not casting) needing concealment or cover to hide. Once the creature possesses the supernatural ability hide in plain sight, the creature can hide in all but the brightest areas and thereafter must be detected normally, usually via opposed skill checks (the hiding creature's Hide skill versus each individual observer's Spot skill).
Once hidden, a creature can do whatever it is hidden creatures do. For those who want to make sneak attacks, that's usually waiting.
Q: Does a creature gain the extra damage from sneak attacks versus foes from whom he's hidden?
A: No. Ignoring corner cases, Dungeons and Dragons 3.5 has two very specific conditions for inflicting sneak attack damage: sneak attack damage is inflicted versus foes who are denied their Dexterity bonuses to their Armor Classes, and sneak attack damage is inflicted versus foes who are flanked. A creature who is hiding meets neither requirement.
What the hidden creature who wants to inflict sneak attack damage does is wait. He waits until the DM declares combat ends. Yes, this is at the DM's whim. Yes, it will depend on the circumstances and the searchers' tenacity.
But then the creature can strike from hiding. The hidden creature will probably gain a surprise round. If he alone gained the surprise round, his foes will be (again, barring corner cases) flat-footed therefore losing their Dexterity bonuses to Armor Class and making them susceptible to the extra damage from sneak attack.
Normally, attacking while hiding requires the creature to be unobserved, have concealment or cover, and suffer a -20 penalty to his Hide skill check. A creature with extraordinary hide in plain sight can attack while hiding while observed. A creature with supernatural hide in plain sight can attack while hiding while observed and without needing concealment or cover. Under normal circumstances, all creatures who do this take the -20 penalty to Hide skill checks.
The opposed skill check (the creature's Hide skill at a -20 penalty versus each observer's Spot skill) made after attacking ("It’s practically impossible (-20 penalty) to hide while attacking, running or charging") can take place after either a standard melee attack or full attack. Ranged attacks are different, though.
Making ranged attacks while hidden requires the character to go sniping:
If you’ve already successfully hidden at least 10 feet from your target, you can make one ranged attack, then immediately hide again. You take a -20 penalty on your Hide check to conceal yourself after the shot.
But "hiding immediately after a ranged attack... is a move action." This typically limits the hidden creature to standard attacks when sniping.
If a lone character wants a fast and reliable method of inflicting sneak attack damage in Dungeons and Dragons 3.5, the supernatural ability hide in plain sight (and, really, the Hide skill in general) isn't it. There are many other ways, though. Get started with a ring of blinking (DMG 230) (27,000 gp; 0 lbs.).
To answer your main question, it is correct that Hiding is part of a movement action, and this applies for Hide in Plain Sight too. If you are not moving when hiding, you still have to use your movement action. From All About Movement (Part Three):
According to the Hide skill description, hiding isn't an action at all, except when you use the sniping option (see page 76 in the Player's Handbook), in which case hiding is a move action. For all practical purposes, however, you hide as a move action or as part of a move action. That is, if you're moving, you hide as part of your movement (something like drawing a weapon, see Part 2). If you don't move, it still takes you a move action to hide.
It must be said that you could however decide to take a -20 penalty and try to hide while attacking (as stated in @Ernir 's answer), even if I would not advise it at lower levels.
You still need some sort of cover or concealment to hide (it may vary: Rangers can use any sort of natural terrain; ShadowDancers and Assassins can use any shadow but theirs, and so on), but being observed by your opponent is not a problem anymore.
Given what I've said above, if you are hiding you cannot Full Attack your opponent: hiding and attacking the following round could be a more desirable option (depending on how many attacks can you land with your Full Attack).
If you succeed in Hiding and can Sneak Attack, every attack in your Full Attack will be a Sneak Attack! From All About Sneak Attacks (Part Three):
Number of Sneak Attacks
Provided it is possible for you to make a sneak attack at all, you can make multiple sneak attacks when you use the full attack action. For example, if you have a higher initiative result at the beginning of an encounter, your foe is flat-footed and every attack you make is a sneak attack.