I have a property that I rent out, how do I get more property?

You buy the other property (duh).  Possibly you could get a mortage on the first investment property or on the place where you live (plus,maybe the place you are buying), or take the money from earnings, or whatever; but you buy the 2nd property and then sell or rent it out.  If you plow the majority of the rent from the 1st property into a 2nd property and get a mortgage as well then you'll have enough for the next property before you know it.

The more places you get, the more you can save, but as you get more places it'll be harder and harder to get financing for the next place (at least to get it from a bank becomes harder).

This is the kind of thing you can do for 20 year plus and then maybe you'll have enough places to retire.

Remortgage your rental, or apply for a new buy to let mortgage using your current rental as equality both which should provide you with money to purchase a new rental..... however be aware of the high taxes you will have to pay on purchasing another property

You apply for a buy to let mortgage and buy another one.

Buy-to-Let mortgages are available in the UK. So search the term.

If you want another property, you'll need to buy another property....