How does it work?

Right now i have a max lvl 30 Common Pet

I want to level it up more! But, how can i "evolve" or w/e him to an uncommon pet and ect.

u should read this
https://forums.wildshadow.com/wiki/realm-mad-god/pets

u can fuse pets, but make sure to fuse ur max common pet with a max common pet of the same family
the first pet will stay and keep the abilities
dont fuse ur maxed common with an unmaxed common
and so on... read the link above and if u still have questions, after reading the wiki, replay here and u'll get help
i just dont want to explain it from scratch (i hope scratch is the right word )

here u can simulate fusing pets
http://pfiffel.com/pets/

Every pet "tier" has it's own level cap. common is 30, uncommon is 50, and rare is 70 and so on.
the only way to get maxed caps is to combine two MAXED (level 30) pets. The ability you want to keep is the one on the left pet. all the abilities on the second pet are lost / irrelevant. The only thing is that both pets need to be in the same family.
getting to uncommon unlocks your pets 2nd ability. You will most likely not get to divine (3rd ability unlock) so try to get the skills you want in the first two slots. The best imo are Heal and MP heal.
when combining two pets that have more than one ability each, the second ability doesn't matter in the cap calculation. So if you have a level 50 unc + level 50 unc you are sure to get a rare 70 cap pet. However, it costs a LOT to feed your pet at that point and you're better off maxing the second ability of both pets before fusing them. Example :
pet1 has 50 and 30, pet2 has 50 and 40. it will make a pet with 70 cap. first skill will be at 50 and second skill will be at the median of the two (35). Considering it costs 30fame per feed per pet before fusing and 100 after, even if you're feeding two pets instead of one, that's still 60fame instead of 100.
Make sure you feed items with 150-300++ feed power, UT's are best to save your fame.

Now you will want to know which pet has the better chances of getting heal and mp heal. Humanoid is the answer. It's always heal ass first skill. Find a few humoid eggs until the second skill is mp heal and then pimp that fker out.