Hi, Take some time and do some research on the different types of beds such as memory foam and spring pocket coil systems.
Then go to a reputable mattress store in your area and take a look at what is available. A good salesperson should be able to provide you with a lot of information about the different beds. You need to look at materials the mattress is made out of, firmness and size you require.
Take into consideration your budget and don't be upsold anything that you cannot afford.
Keep in mind your sleeping style do you sleep on your side, stomach? Do you need a lot of personal sleep space if you are sharing the bed with someone else a king, queen or double.
Be sure to try the beds out and make sure you know their return policy. There are some stores that will let you return the bed within a certain time frame if it is not working out for you.
This is important as who can really tell from lying on it in a store if it will be right for you for a whole night. My friends thought they wanted a firm mattress but are miserable on it and didn't buy from a store that would let them return it. Take a look at some consumer reviews on the Internet at amazon or consumer reports(can also look at at your local library). Take your time as sleep is important for your health and how you feel during the day. Since you spend a 1/3 of your life in bed you should spend some time getting the right mattress for you. Hope this helps.