Google Adwords is the most popular method for traffic. Since they are the top search engine right now it make sense to advertise there if you can afford it. You bid on keywords to get your site at the top of the search when your keyword comes up. There is more involved but it's all laid out at Google. There are a lot of other sites that use this advertising strategy called pay per click or PPC.
Not all web traffic is welcomed. Some companies offer advertising schemes that, in return for increased web traffic (visitors), pay for screen space on the site. There is also "fake traffic", which is bot traffic generated by a third party. This type of traffic can damage a website's reputation, its visibility on Google, and overall domain authority.