You can either set out to do some casual raiding or become a progression raider.
If you want to do progression raiding, apply to join a progression raiding guild. Trying to start from scratch yourself would likely be too much to handle from what you have described about yourself.
Progression raiding is about advancing through the toughest content and is more about being part of a team (think of it being like semi pro football, well pro even if you are in a raid team that breaks new ground). Takes a large amount of dedicated effort and time and a lot of self discipline to be any good.
It usually involves getting keys/flags both individually and as a raid force to gain entry to the "next level". e.g. PoP flags, GoD keys, MPG Trials, DoDH flags etc.
Casual raiding is more along the lines of a family/casual guild, getting together occasionaly to hit isolated targets for fun and equipment upgrades. DoN Dragons and TSS Dragons being the most likely targets atm.
If you were to try and form a casual based guild and go raiding for the first time, start with outdoor type zones where corpse recovery is not a big drama and you can afford to take a few goes at something while you refine your tactics. The DoN and TSS dragons may be a bit tough if the raid team's equipments is not at top end bazaar level, you could start with OoW mobs like Velitorkin in WoS, Bonecracker in Nobles and Lihra in RCoD.
I'm not so sure that tagging along on a pick up raid would be a lot of help as you will either have a raid leader who knows exactly what he/she is doing and you will be told to run here go there stand still and the raid will be over and someone will have looted something. Or, the raid leader will have no clue you will die multiple times, wonder what the hell is supposed to be happening and someone will loot something and you'll be told that the raid is over. :P