It very much depends what kind of mediation you mean.
If it is with neighbours, for example, over noise/nuisance etc your local authority may well have a scheme that you could use that should not be expensive and may even be free.
For family mediation/divorce then a solicitor could arrange it or do it, or social services might be able to help. Any campaigning group or charity in the field might have information.
For any other kind of legal or commercial dispute, a solicitor is again the best first port of call to find someone good in your price range with experience of the area in question. The cost varies very widely, with a CEDR-accredited mediator probably being the most expensive (see their website for more information).
Many solicitors and barristers do mediation and most will do it for a set fee you and the other party would share. It can often take place in their own offices or your lawyer's office, saving the cost of hiring somewhere.
For any dispute I would recommend using someone who is a trained mediator and has good, relevant, experience.