Testing companies AncestryDNA, FTDNA, MyHeritage and 23 and Me all offer affordable DNA testing kits and return results within a few weeks.
The size of the database and the background of the people in their testing pool will determine the number of DNA relatives you discover.
A word of caution, the better documented your family tree, the greater the success of identifying your DNA relatives.
Companies like GEDMATCH and FTDNA aggregate DNA results from a number of different testing companies. By uploading raw DNA data from one testing company to these sites, it increases the total number of DNA relatives.