Paying the full price
If you decide to pay the difference of magic item's Price, then this difference already includes both the magical components and his spellcasting services. The magical components cost is always half the market price of the item, everything else is profit for the creator/seller.
If you have a Belt of Incredible Dexterity +2 (4,000 gp), and want to upgrade it to a Belt of Incredible Dexterity +4 (16,000 gp), the 12,000 gp difference already includes the components and services.
But if you want to save some money, you could buy the required reagents for 6,000 gp and look for a spellcaster to upgrade the item for you.
You can simply go to a wizard with the reagents...
and pay for his services
Yes, unless said wizard is a friend and wants to work for free, the Cost of a magic item is simply the Magical Components required to craft the magic item, or upgrade the item.
Cost: This is the cost in gold pieces to create the item. Generally this cost is equal to half the price of an item, but additional material components might increase this number. the cost to create includes the costs derived from the base cost plus the costs of the components.
Now, if you read the rules for cooperative crafting magic items (on that same page), you will see that for each day spent crafting, one of the creators (or yourself) must provide the spell required for that magic item, or suffer an increase of +5 to the spellcraft DC per spell missing.
For convenience, i will quote those rules here:
Requirements: Certain requirements must be met in order for a character to create a magic item. These include feats, spells, and miscellaneous requirements such as level, alignment, and race or kind. The prerequisites for creation of an item are given immediately following the item's caster level.
A spell prerequisite may be provided by a character who has prepared the spell (or who knows the spell, in the case of a sorcerer or bard), or through the use of a spell completion or spell trigger magic item or a spell-like ability that produces the desired spell effect. For each day that passes in the creation process, the creator must expend one spell completion item or one charge from a spell trigger item if either of those objects is used to supply a prerequisite.
It is possible for more than one character to cooperate in the creation of an item, with each participant providing one or more of the prerequisites. In some cases, cooperation may even be necessary.
When you ask someone else to craft or upgrade an item for you, you can provide all the components, but that doesn't mean he will work for free (unless you convince them somehow), and you will have to pay for the spellcasting services(normally Caster level × spell level × 10 gp), which may or may not be available on that town, based on it's population and size.
This cost must also be paid when you request a npc cleric to cast spells on you, or when you ask a npc to use a divination spell to ask questions about your quest, or when you need a npc wizard to enchant your masterwork sword with a +1 enhancement bonus.
Of course, if you are the creator, and provide all requeriments, you do not have to pay for any extra service. But if you need the aid of someone else, they may charge for their availability.
On your example, you can pay 6k gp for the materials, provide the base item (Belt of Incredible Dexterity +2) and would still need to pay for it. "How much?", you will ask your GM.
To craft this item you must be at least 8th caster level and be able to cast cat's grace, either that or have enough ranks in spellcraft to beat a DC 18 (not that difficult), but for the sake of this example, let's say they only need to be able to cast cat's grace and be 8th level caster (could be a wizard, or cleric, or anyone able to meet those requeriments, really).
- Spell Level: 2nd x Caster Level: 8th x 10 gp: 160 gp
So 160 gp is the average cost for each cast of cat's grace from a generic spellcaster. Since the upgrade has a cost of 12,000 gp, that means he will spend at least 12 days working on your belt, so he may charge you 1,920 gp for all the trouble.
Note that this is still cheaper than buying 12 scrolls and cast the spell yourself if you don't have that spell.
This example is probably the most expensive you could go, working with your GM and rolling Diplomacy, you could make this go lower. If you have the feats but not the spell, you could find a 3rd level spellcaster to cast it for 12 days and pay only 60 gp per day (720 gp total) instead.
The spellcasting service's formula is an average market value for that kind of service, the GM can lower or increase that cost based on any circunstances he sees as necessary. But this cost should never be the same as what he would profit from using his own money to craft the item and sit it on his shop waiting for someone with enough money to buy it (that could take months to happen).
Usually, spellcasters that work on a town, are more than happy to sell his spells and time, as the average earnings for downtime is about 2-4 gp a day. Unless, of course, he is already working on another project and cant cancel it (or all his progress is lost)