It's a good idea in the UK to arrange a mortgage with a bank before you start looking. This is when the bank tells you how much money they will lend you so you have a good idea of how much you can afford.
The next step is to go to an estate agent to see what sort of properties they have available in your budget range and in your area. If you see something you like, the estate agent will arrange for you to view the property, so that you can see the house or flat for yourself.
If you see something that takes your eye, you put in an offer. The vendor can accept or decline this offer, and if the vendor accepts it, you can move forward with the sale. However, as you don't pay any money at this point, the offer isn't legally binding, and in theory, you can pull out of the offer at any time that you like.
Your next step will probably be to get a structural survey done. A qualified surveyor will inspect the house and write a report that illustrates any structural problems, like damp or drainage problems.
If you still want to go ahead with the sale, you need to appoint a solicitor to do the conveyancing. If you already own a house, you might also be busy trying to sell it. Many house owners prefer to sell to first time buyers, as they are not in a chain.
Finally, once the contracts are signed and exchanged, you complete on your house. You get the keys and you can move in whenever you want. Then you