As a PP said, Head for Points is your first stop, loads of fantastic info. I found it all mind-boggling to start, but I am in the swing now.
Places I collect points include (I will have forgotten some, no doubt):
Flights
Petrol (Shell)
John Lewis and many other stores through Gate 365 on Exec Club
On my credit cards
Topcashback converts to Avios for most retailers
Clubcard points
Some places are easier to book flights to than others. I don't recommend Cape Town to start with, you may lose the will to live ... New York and the like though seem much easier. I have my business class flights booked for September though (you still pay the taxes, so it is effectively equivalent to paying to a decently priced economy flight, but getting BC/FC travel).
Depending how dedicated you are, some credit cards it may actually be worth paying for.
The AmEx BA ones come in two versions - free, with a reduced Avios intro bonus, standard collection rate and a 2-4-1 voucher that only has 1 year validity before expiring. The one you pay for (£195) a year has an increased collection rate and the 2-4-1 is valid for 2 years.
For those places that don't take AmEx, I have a Tesco Clubcard credit card, so at least I get some.
If anyone wants referral links for the AmEx, feel free to PM me LOL. The referral link slightly increases the amount you get (after spending a set amount over a set time, which presumably varies across the cards but will be clearly set out) and I would get a small bonus too.