Advertising can be done online at many different places. There is no marked single best place for everyone. Depending on the type of website you own and the portion of market you are targeting, the best place will vary. Experiments can be done among carefully chosen advertizing destination, before you can find the right place to advertise.
Google AdSense is one very popular place to buy advertising online. Rather than having to pay a large amount up front as with banner ads, you can simply pay a few cents for each click you receive on your ads. You'll be billed monthly, although Google may periodically charge your credit card if they feel your balance is too high.
Advertising on blogs by means of ad posts is a great way to advertise. You should carefully choose a blog that is relates to your site in nature. If your site is an ecommerce site that sells computers and electronics, then you should advertise on technology blogs, instead of sports or politics blog.
Ads through CPA companies like Rocket Profit and Market Leverage can be bought. They offer you many different ways to advertise, e.g. paying per click, pay for email addresses, pay for postal address or telephone submissions, or for sales. You can figure out which option best suites your need and then pay for the selected option.
You can create traffic to your site (if you're selling your own product) by starting an affiliate program. People who sale your products can be paid accordingly, instead of having to pay for each click, no matter if you don't make any money out of it. Affiliation program can be started on your own server with scripts, or you can go through already existing solutions like Commission Junction.
Well known social networking destination Facebook sells targeted advertising. You can use Facebook ads, if you're looking to target specific groups of people. These ads are not very expensive to set up, and they can create great amount of traffic if targeted correctly.
Remember, there is just no one best solution for every site. You might advertise your site on AdWords and have exceptional results, while a friend of yours with a similar site has very poor results from the same source of traffic.
Research well the demographics of the market you wish to target, and then search for an appropriate advertising method that is supposing to targets that specific demographic well. You will achieve great results you're looking for, only when you target the correct audience for your website.