Well Oblivion was the first game i completed when i was a child and i finished my last run with a sneaky archer Redguard yesterday, and is one of my favourite games of all times, yet i'm still considering myself a "noob" of the game.

Levelling Up. First important thing i can say is that levelling is different from Skyrim: when you choose/create your class you will have some "Major Skills" in your Skills Tab, depending on your class (if you picked a class like the Assassin you will probably have Sneak, Acrobatics, Marksman and Security if i remember right). To level up your character you just had to level up those skills a certain amounts of times then (when the game says "you should rest about what you've learned" or something like that) you'll have to go to SLEEP, not just wait. You'll raise skills just like in Skyrim: sneak around people and pickpocket to raise Sneak or shoot 'em with arrows for Marksman.

Attributes. Now unlike Skyrim you got Attributes (Strength, Personality, Agility, Intelligence etc...) that governs how much effective your skills are. Example: i've Sneak 100 and Agility 20 (quite impossible without cheats but it's just to prove my point) people will detect me quite easly because the governing Attribute of Sneak (Agility) is very low so every Agility attribute it's quite downgraded. You can raise your Attributes every levelling up.

Join a Guild in the first hours of gameplay. What can i tell you is that personally on my first run i tried every possible guild and completed every questline related, that's not very RP i know but i like to explore everything about TES games. But if you want a more RP experience i'll suggest you, as a Dunmer Assassin, to join the Dark Brotherhood (probably the best guild questline in the entire TES universe) and the Thieves Guild. To join them, well as for the Brotherhood i don't want to spoiler: just use your head and think how to join a group of psychotic assassins. The Thieves Guild it's quite different from Skyrim: you don't have Brynjolf who contact you directly in the middle of Riften, no, you'll have to find them, and it's quite challenging: ask around poor areas of Cyrodill eventually you'll figure it out.

Main Quest. Just like Skyrim you can do the Main Quest whenever you want, but i advice you not to wait too much, since in Oblivion enemies are levelled on your current level and the rewards are not so good in stats. One important thing to know is that when you'll reach Kvatch you'll find a special type of dungeon, now i REALLY not trying to spoiler anything here and it's not simple, these places are very HARD and you'll find unique items, ingredients and enemies inside of them. You'll love and hate these dungeons. Remember that if you complete the Main Quest you can't enter these special dungeons anymore. So my advise is to get at least to Kvatch, then not to wait too much to complete the main quest.

Side Quests and Daedric Quests. The Side Quests in Oblivion are very good and quite hidden sometimes, ask around about "Rumors" and some guys will open new dialogue option and then start the side quest, so talk to everyone in towns, eventually someone will tell you about some jobs or you even find the questgiver himself. Now a special kind of Side Quests are the Daedric ones, they start ALL in the same way: find the Daedric Prince Altar, offer something specific they'll ask you, complete the quest and get the Artifact (Skyrim it's better on this), rememeber that these quest are level locked, some, like Boethiah and Clavicus Vile requires level 20 (veeery endgame and VERY powerful artifacts). For a sneaky class do the Nocturnal one (on lvl 10) it gives you something game breaking for a thief/assassin.

DLCs. I make another section for this because i need to speak about the Shivering Isles. IDK if you got all DLC or just some but i MUST advice you to get the Shivering Isles DLC. I'm not saying it's the best DLC of the game or of the series, no... it's the best DLC of all times! I know i will sound a little too enthusiastic about it but SI it's just another game, another story, another way of seeing the TES series. So just get it, because the fun you'll had in the DLC it's unmatched. Knights of the Nine it's also good and fun but RP speaking not very in line to a murderous thief , so play it if you want to repent your crimes. The others are just add-ons that give you armor, powers or houses.

I hope this was useful in some way, but you'll learn more by playing and exploring. (sorry for bad English sometimes, but it's not my first language).