I'm pretty new to playing D&D, as are most of the people I play with. We found some homebrew race stuff already and one of us is playing as a Khajiit, but I wanted to play as a Cloud Giant and I'm not sure how to go about doing that. Is there a known way to adapt monsters to playable characters? One thing I've already said is that he was an outsider because he never grew enough (6'8") which takes care of the size issue, but I have no idea about anything else.
Take it slow...
Since you're all pretty new, it's generally considered to be a really good idea to stick with the official published rules at first, so you can see how things play out and the effect of different abilities before you start messing with them in ways that might change the game balance.
If you really want to play as a cloud giant runt (which does sound pretty fun), what I've seen done a couple times is you pick a race from the Players Handbook, and use those ability scores and traits, but just call it a cloud giant. You get to indulge your imagination while making sure you don't have an unfair advantage over other players (the instinct to design a super powerful race is tough to resist, I know.)
When you're ready, the Dungeon Master's Guide has guidelines for creating custom playable races.
The above is all standard advice, but you know your group best. Don't let anyone stop you from having fun together. The key to making sure everyone has fun is to check in with the other players before you change something. If people look at your proposal and say "Dude, that sounds awesome, please do that," then you're good to go, no matter what the rules say.
One of the early characters in proto-D&D was a Vampire (Sir Fang). In fact, the Cleric class was invented as an anti-Vampire (there was lots of PvP: proto-D&D developed from wargaming).
Basically, they built a Vampire "class" that started with one HD, and leveled up and gained more and more Vampire powers.
You could do something similar with a Cloud Giant, where you start as a runt who is still growing, and gain HD and Cloud-Giant like abilities as you gain levels.
This will take care if you don't want to break the game in a number of ways (steal spotlight, for example), and you probably want to have a strong DM and be willing to have your abilities "nerfed" after the fact in case a screw up is made.
Doing this as a race-as-class is generally easier than doing a Cloud Giant race with some random character class, and results in a "more gianty" giant than the alternative.
You'll have to work with your dm to homebrew something. Take a look at the other playable races (especially goliath) and try to make features equivalent to those.
The basics would be +2 to one stat, +1 to another, and two to three other features approximately equal to those features found in other official races (compare to dwarf, goliath, half-orc, etc...)