you will get a better response if you post in the carpet cleaning issues thread above, more people view that forum.
Basics
Sadly a lot of folk think there is a pot off gold at the end of the carpet cleaning rainbow. The reality is it's a long term development business and totally depends on the ability of the operator to do a good job and gain referals whilst also being focused enough to develop a marketing strategy to find the customers in the first place. It's a continuous process for a couple of years until momentum and returning customers start to pay off. I started with a £8000 budget nearly 20 years ago but it would take more than that now.
As a minimum you will need the following.
Training. Machine supplier often offer free training with their machines. National carpet Cleaners Association. Various courses around. £0 - £300. You would be wise to get some insurance too.
Be prepared to spend between £1000 - £3000 for a decent machine. Restormate, Cleansmart, Alltec, Ashby's, Extracta & Prochem can supply various twin vac machines. Alltec, Solutions (cornwall) & Cleansmart can help with tripple vac 500psi + machines. There are often machines for sale on here in the for sale section or you could take a look on ebay. After that hand tools, hoses, chemicals, etc. £500 - £1000, and don't forget you will need a van too.
Marketing and sustainability. You will need a good marketing budget and enough cash for 1 - 2 years as a back up to sustain through lean times. I probably would not start now if I had secure(ish) income or a job it can be hard going. But if do choose to go ahead doing an excellent job so customers refer you is a good way to start.
Do a search for 'what machine' or 'starting a carpet cleaning business' lots of threads.