These questions have been answered many many times on these boards and a quick search would bring up the answers.
However briefly, there are three main types of tests
a) yDNA this test can be taken by males only and gives your direct male line ie father, grandfather, great grandfather etc.
b) mtDNA this test can be taken by males and females and gives your direct female line ie mother, grandmother, great grandmother etc.
c) autosomal DNA sometimes called family finder. This test looks across all your lines and is what is used to find relatives anywhere from your direct male to direct female lines and also to determine your ethnic origins however a word of warning the ethnic origins given in some cases amount to nothing more than badly researched guesses and so should not be taken to heart when they don't say what you want. This test is really only meaningful for about five generations back
Haplogroups are a way of classifying people by looking at mutations to see when one group of people diverged from another. These can be used to track the movements of people across the word
https://en.wikipedia.org/wiki/HaplogroupThere are a number of companies that do tests and prices and competence vary. Most companies do sales every so often. ftDNA.com have a sale at the moment but it closes 11.59pm (CST, Central Standard Time America) 31 August 2016
If you search the web (or wikipedia) you will find details of the companies and some comparison charts as to what tests they do)