Do you have an icon either on your home screen or in the app drawer that says Market or Play Store? Touch this to add apps. You will also need a gmail account to sign into the store with.
Some websites such as Yahoo may suggest that you download their app if you visit them through the tablets browser. Open the browser and go to Yahoo and see if the offer you the option of using the app which will take you to the market page for that app.
Also check if you have an Appstore icon for downloading apps from the Amazon Appstore. If not, you can get one by going here: Amazon.com: Appstore for Android and following the directions in the upper right corner of the page.
What kind of tablet do you have? It may not come with the Play Store or even be able to run it. You may need to use a third party app store. Often times people who cant get the Android Market/Play Store to work on their machines have luck with the Amazon App Market.