There are three ways. Firstly, you can send a sample to a lab and have it tested for you. This will give a technically accurate result, assuming the sample you sent was representative of the whole area. It usually costs a bit more to have a lab do a test for you than it does to buy a home test kit. It is less work however, and a good lab will provide some advice as well as the result itself.
As an alternative, you can get an inexpensive kit from the Garden Centre that will give quite a reliable result. The usual arrangement with this sort of kit is that you put a bit of soil typical of the area that you want to test in a little tube, then you add a few drops of test solution, shake it up and leave it for an hour or so to settle. Once it has cleared, the solution in the tube changes colour according to the pH of your soil, and you compare the colour with a chart that comes with the kit. Different kits work in different ways, but usually acid soils give a kind of yellowy-orange result, and alkaline ones give a greeny-blue result. You usually get a colour card, rather like a paint colour chart to compare the colour against to give you the result. The better kits also provide advisory booklets about how to interpret your result.
The third, and least reliable method for the inexperienced gardener, is to use the plant lists to identify the sort of weeds and plants that grow well naturally on your soil. From this you can often develop a good guess as to what the pH of the soil is. For example, knowing that cabbages and wallflowers do well in your garden, but Rosemary keeps dying off would lead you to the view that the soil is alkaline (Cabbages like alkaline soil, but Potatoes prefer it more acid).