The Respecification lets you change the powers within your two powersets and the pool powers you picked as well as where you placed your slots. It doesn't let you change your two core powersets.
Edit: Be careful what you change and try out the new build on the test server first before finalising it on live.
The Respec Trial can be undertaken 3 times, the first of which becomes available at lvl 24 and needs a minimum team of 4 (though I'd personally suggest a couple more than that). The contact is in Independence Port at the end of the Terra Volta bridge (the far end from TV).
There tends to be a lot of strange rumours and tales about how to do the Trial but treat it like a TF and you should be fine. 
Not sure about the last question though... would be a good fight though... 
For your 1st Respec mission you need to be at least level 24 and it caps at level 32. I'd recommend going around lvl 28-30 with either a full 8-person team, or a 5 person team (as the mob size changes when you to 6 people)
Go to Independence Port and see Jane Hallaway She stands at the corner of the road at the Northern (upper) end of the big main bridge where the road turns West. You need at least 4 people minimum to start.
Once eveyone in your team is in the Independence Port (all team memebres must be in the same zone to start any TF) you can start. Talk to her and she'll give you your first mission
1. Speak to Jason Serano - Located in Terra Volta
NOTE: Be sure to have your leader of the Task Force stay next to Jane Hallaway so you are not taking so much time going to contact and back.
2. Get Sky Raiders attention Defeat 25 Sky Raiders in Terra Volta
NOTE: Best Place to kill Sky Raiders is in the North-West corner of Terra Volta there are plenty of big groups there.
3. Defeat Sgt. Clayton & his men This missions location is Random I have done it where this mission is placed in several places. Keep your eyes peeled for big green crates that are clues. When targeted they are called containment equipment. EDIT: Not seen crates before basically find the room where the Sgt is and clear out the room. If you have someone with Invisibility and Teleport Friend they can "ghost" around the building til they find him, then teleport everyone else to their location. Clear room, mission done.
4. Save the Terra Volta Reactor
Alright now you have made it to the finale. But beware, once you walk in through those doors, you will find a group of enemies harassing 2 guards, once you save the guards they will open up doors to a Big room.
- Once inside the big room you should defeat all the enemies so no enemies are harassing you once you get inside the smaller rooms. BEWARE: Inside the Big room at the back to the left corner is an explosive that will blow up if someone blasts at it or goes near it. I would recommend that you send your tanker (if you have one) to taunt all the enemies into that corner so that when the explosives blow it will damage all enemies around it.
- When you are done clearing the bigger room you must go through every door except the one that leads to the reactor core, and save all the scientists inside the rooms. At one point a scientists will give you the Reactor Core Key card that will let you get to the Core. EDIT: Once you have the key you don't need to clear any of the smaller rooms.
- Once you go through the doors to get to the Core, you will find yourself inside a giant corridor that will wind around to the core. BEWARE: along the walls of the corridor are explosives. EDIT: Just blast them from a distant or get a tank to take the damage
- And now you have reached the Core! But before you go inside through those doors you must grab a few goodies. To your right will be a machine that gives you a red bubble that will resist all damage from inside the Core. NOTE: Bubble does run out so you will have to go back and recharge it. To the left will be a shelf of guns, that when fired at the Reactor Core will heal it. NOTE: You get only 20 uses of this temporary power. So use it wisely. EDIT: these "guns" are actually Coolant Belts and give you a temp power called "Coolant" make sure you have it ready. There is always fewer Coolant belts than team members so some will miss out. Don't heal the core unless necessary those 80-120 odd "shots" between your team may become necessary much later. Stand in the red bubble maker awhile to get a red radioactive bubble. It runs out about every 5 minutes so just replenish it (run back to the machine) between waves of enemies.
- Now once you are inside the Core you will be pelted with wave after wave of enemies that will come out of doors on an upper floor. There is no pattern as to how they come out. You just make sure that you and your team can survive the enemies.
EDIT: If the Core starts to look low (just target it to see its hit points) then use the Coolant power to "heal" it.
When it is all over and done you will receive an option of a bunch of rewards. They are a free Respec, or one of many different types of Enhancements. If you choose the free Respec you must go to Jack Wolfe in Galaxy City, at Freedom Corps (inside the Freedom Corps building behind the Trainer, he's on the right just in side the building). At the end you will also get a couple of badges to go with your exp. You get: Transmogrified, Received the Stalwart Medallion.
WARNING: You only get to choose a Respec ONCE per Respec Trial, so once for lvl 24-32, again at lvl 34-42, and so on. In other words say at level 24 you do the Respec. If you do the Independence Port 1st Respec Trial again you wont get to choose Respec as a reward again. You'll have to wait until level 34+
I took all this info from Game Amp. Just go to the main site for CoH and choose CoH Trials from the list on the left-hand side and click on Jane Hallaway's detailed notes
http://cityofheroes.gameamp.com/coh
Tips: The level of the mobs are decided by the highest member in your team. If you have a level 30 then they'll be 30, 31 up to lvl 31 bosses. This makes it tough. Best thing to do is try to Exemplar high players down so everyone is at a lower level. Start the Respec Trial and STAY Exemplared through all the minor missions until you get INSIDE the Terra Volta Reactor building. Once inside, switch all Exemplared players around to Sidekick anyone they can. This makes the mobs in the Reactor core set to the Exemplared level you had when you entered but now the team is punching at a higher level.
Any other problems I'd post a question in the "Player's Question" forum. Plenty of help there.
good guide Sion..can i just add set your rep to heroic!!
Also the reactor spawns at +2 to the highest team member as i found out yesterday 
If your looking to do it tonight (Friday) give me a shout @dipstar
Nice guide! A few extras:
- The glowy crates in the Sgt Clayton mission are actually coolant belts; the more of these you click on, the more you get offered outside the reactor core. But if you don't click on any of them at all, the game seems to decide you're a team of noobs that needs all the help it can get and gives you a full 8 coolant belts. 
All or nothing, decide which way you want to go!
- If someone has TP Foe much fun can be had by porting the reactor building proximity bombs into mobs and using a ranged attack to set them off.
- Even if you find the key at an early stage you might want to clear all the other rooms off the main entry hall. If you face TPing mobs in the core and one decides to take up lodgings in an unopened room it can be a mare to find them.
- On a related note, if it seems like it's been way too long between waves there may be a runner/TPer in the reactor corridor or beyond. The next wave won't start until the previous one's been completely cleared, so send a good soloer toon to check things out!
- The reactor core's pretty robust, and the number of heals the coolant belts grant you is limited (each one does a lot of healing though!). Try to restrain yourself from healing the reactor every time it takes a little scuff, just give it a burst when/if it goes under 50% health, or top it up between waves.
Dang, I should have mentioned something about the reactor area and the necessity of selecting the Respec as your reward on completion.
I knew I'd forget something.
The above posts are good guides though.
Who is this blue eyed Thing? I used to read X-Men alot but have been quite out of it for the past five years so i have no idea when Colossus might or might not have had a fight with her. Tell me more plz.
The ever-lovable Thing!
Fantastic Four character. Grumpy and fun.
Good Afternoon all
Idiot question number 2, Whats a respec, I understand it allows you to re-design your hero, and I gather via the boards that to do this you complete a Task Force is this correct? Which one etc?
Is this true and is there anything else I need to know?
Thanks in advance.
On a different note, after a conversation between my brother and myself last night. Has there ever been a ruck between the baby blue eyed Thing and the X-mens Russian tractor boy Colossus? and who won? this occupied an hours worth of our time in the pub last night (In between the bandit and a bag of crisps- prawn).