Step 1: Talk to a mortgage broker and find out what your options are likely to be and how much you can afford from the bank's perspective (they will usually offer more than you should *really* borrow, so be mindful of this and decide what your comfortable with).
Step 2: Start looking at homes
Step 3: Offer, acceptance, hire a solicitor, have a survey, wait many many many months while no one does anything
Step 4: Deal with the sellers saying they've had offers from other people offering more money. You either match it or beat it. This could be all lies, it's impossible to know. At this point you will have already spent a few thousand pounds on solicitors and surveys. There's even a term for it - gazzumping!
Step 5: Exchange contracts - this is when it's finally all legal and you give your deposit over.
Step 6: Completion. It's not unusual for exchange and completion to be on the same day.
Learn about chains and pray you aren't in one.