If you get the info fromt he HFEA website on clinics that do egg donor treatments, you can call your nearest one and they will set you right.
The whole thing will take about 7 or 8 weeks of hormones - could be a sniffer plus injections, or just injections. Beforehand, you will have to have a set of blood tests for things like HIV, HepB+C, FSH, LH, prolactin, progesterone (maybe) and a couple more. You'll need to go in for scans, and towards the end when you're doing the stimulating injections (once a day) then you could be going in daily. It's quite a big committment in terms of time. Once the eggs are there, you'll go in for minor surgery to remove them: mine was done by inserting a collecting needle through the vaginal wall to the ovary. You will be under heavy sedation though...I have no memory whatsoever of it (thankfully!)
The way the law stands, when any resulting child reaches 18, he/she has the legal right to know your name and the address at which you lived at the time of donation. It is not handed over just like that, the child would be counselled through this in some way. Of course, they will be able to trace you probably quite easily...
People worry about half-siblings meeting and marrying/having children: basically, if the child knows he/she was conceived as the result of donated gametes or embryos, they can check with the HFEA to find out if their intended partner is related to them. (I think they get a yes/no answer rather than your details if it's a yes.)
Ovarian hyperstimulation syndrome (ohss) is a risk, albeit relatively rare, but bear in mind that there are differing degrees of it and clinics are on the lookout, you will be given information on symptoms, called to see if you're ok, and advised to drink loads in any case. OHSS can happen, but the very serious, death-inducing degree is extremely rare and I think the last time it happened the clinic was sued because they didn't respond to the woman's worries, ie were negligent. TBH I had heard it could cause ovarian scarring but I didn't know about premature menopause. I haven't heard that one.
I have a friend with twins from donor eggs and went to donate myself (they wouldn't let me because I'm still holding out for another baby). It would be a wonderful thing to do.