Thing is, adon's moves are good if they hit and they do have good priority, but for the most part, they are mostly unsafe (as in if the other person blocks your move, they have time to get a free hit off you) and his combos are really hard to time. Arcade mode is good for getting comfortable with your character and practicing combos and moves, but they are so brain dead compared to real opponents who probably knows how to block. 

They seem daunting to a newcomer, but try to do as many trials as you can. They'll help you learn your basic combos. If one is driving you nuts, skip to the next. Do them whenever you get a chance, even the one's you've already done.
 
As for Adon specific tips, I only have a few:
-His standing hard kick is a great tool to keep people away. It comes out pretty fast and has insane reach. Throw it out there every once in awhile.
-Crouching fierce punch is another good poke. Does okay damage as well. 
-When up close, learn how to quickly combo into your rising jaguar and then get out of range. Mix it up. 
-Mix up your jaguar tooths as well. You can fake someone out by hitting the light kick version and just landing near the wall.

Adon is all about mind games, using different reaches of his jaguar tooth and kick (with the different kicks). He can be both very predictable, or very unpredictable. He's also very special move dependent, he doesnt have many combos or links. I love him, but most people hate him (and most people don't know how to use him to be fair)
 
For a first street fighter game, I wouldn't recommend him as a first character

Ive been thrashed by a good few Adons online and funnily enough he was also the only character in Arcade to give me any trouble (even more than seth)  
Agree with what others have said here, he can be very unpredictable at times which seems to be when hes at his most effective - all the advice Rhaknar gave in the post above this should give you a good indication of how to 'Up' your game!

" I recently bought the 1st street fighter game of my life and after messing around with a number of different characters. I decided that I liked Adon practiced by doing the arcade mode for him, I hopped online and am keep getting my arse handed to me repeatedly. It maybe because I am rubbish but do any Adon players have any tips or are playing SSFIV on the PS3 so I can look you up? "

" Thing is, adon's moves are good if they hit and they do have good priority, but for the most part, they are mostly unsafe (as in if the other person blocks your move, they have time to get a free hit off you) and his combos are really hard to time. Arcade mode is good for getting comfortable with your character and practicing combos and moves, but they are so brain dead compared to real opponents who probably knows how to block.  "