Doing the IRATA way there are 3 basic ascender rescues and a few descender rescues.
bearing in mind rope access uses two ropes, a working line and a backup line so you can ascend / descend their backup line if need be.
the descender ones are simple.
1.get above them, descend to them,
2.clip into them,
3.lower them onto you and remove their descender.
4.decend to ground using an additional braking carabiner.
Ascend rescues, there are three, beast, counterbalance and snatch.
i'll describe them as if you are coming down to the casualty on a seperate rope system.
Beast
1.descend on a seperate rope and change from decending gear into ascending gear,
2.clip into them,
3.start climbing until their croll goes slack,
4.install descender and change from croll to descender
this one is super tough on the legs as you are climbing with 2 people.
counterbalance,
1.descend to casualty,
2.tie into casualty,
3.attach a hand Ascender (jammer), shunt, prussic above casualty on their rope,
4.stick a carabiner through the bottom hole / prussic loop
5.thread a sling / footloop through the carabiner on jammer etc and clip it into their d ring,
6.stand up in footloop / sling, this equalises your and their weight,
7.grab their harness and pull up
8.still pulling up, disconnect their croll and lower onto your harness
9.descend to ground
Snatch
1.Descend to them,
2.clip into them,
3.attach ascender above you with a carabiner on the bottom hole (a shunt or prussic would work too) thread the rope through carabiner (a pully on this makes it easier).
4.Attach a second ascender (robbed from the casualty) and half the footloop length (or use a slingor a pantin.
5.Use this mechanical advantage to start climbing
6.when their line goes slack remove their croll,
7.remove your extra gear and descend.
hope that helps.
there are additional IRATA rescues but they are variations, i wont decribe them as you are unlikely to encounter an aid climb, deviation, rebelay or loop up a tree.
Jamie