The most basic way to find out your general soil type is to dig a small pit and pour a bucket of water into it. If the water is reluctant to drain away, the soil is likely to be clay, but if it drains rapidly then it's a sandy soil.
To get a more accurate idea of your soil type, take a small handful of soil and wet it. Knead it between your hands and try to form it into a ball. The following results will reveal the soil texture:
Sticky and gritty – loam, the perfect soil!
Easily rolls into a ball, but feels rough – clay loam
Easily rolls into a ball, shiny when rubbed, but still gritty – sandy clay
Easily rolls into a ball and becomes shiny but not gritty – clay
Doesn’t roll into a ball well, and feels gritty – sand
Easily rolls into a ball but it falls apart easily – loamy sand
Feels slippery and silky – silty loam
Soil type affects how well it retains water and nutrients. Clay soils hold onto water and nutrients for longer, so tend to be very fertile, but have the disadvantage that they are heavy to dig and can bake hard in summer. Sandy soils are easy to work but water and nutrients wash away quickly. All soil types can be improved by regularly adding more organic matter such as compost, manure or leafmold.
It's not usually essential to buy a soil test kits to find out the pH and nutrient content of your soil unless you want to grow things like blueberries and cranberries which need very acidic (low pH) soil, or if you suspect that your soil is lacking a specific macronutrient (nitrogen, potassium, or phosphorus).