The easiest and least time consuming option is to 301 redirect the old domain to your existing site. This tactic obviously works best if both sites are in the same sector and are targeting the same keywords; otherwise, if you have a pet supply site and you buy an old Texas Hold 'Em poker site, a redirect probably might raise some eyebrows among the search engines. If, however, your site is brandnamepets.com and you buy onlinepetsupply.com and 301 redirect the domain over, you're inheriting a lot of topical and appropriate links.
There’s an important distinction to make here between domain flipping and website flipping. The latter mainly refers to buying and selling full websites. By full websites, I mean websites that actually have content and more often than not have traffic and revenue. When buying and selling websites, the domain name matters less as the main value there is the content, traffic, revenue, history/reputation, sustainability and growth opportunities. The same can’t be said for domain names where you’re just selling “the name” and hence it’s all that really matters.