Oak Chips & Cubes
Probably the most common way that homebrewers introduce oak flavor to their beers, and available through most homebrew supply stores. Chips and cubes come in different oak varieties, such as American, French, or Hungarian.
American oak is more aggressive with its flavor and adds some vanilla notes, while French oak is more delicate and adds some spiciness. Hungarian lies between the two. In addition to the varieties, chips and cubes come in various degrees of toast - light, medium, and heavy. The degree of oak flavor to depart will depend largely on the style you're brewing and on your own personal taste.
Both chips and cubes are usually added to the secondary fermentation after sterilization by boiling for 15 minutes, or by soaking for several days in alcohol (e.g., whiskey, bourbon, or vodka). By soaking in a particular alcohol, a homebrewer can attempt to mimic the barrel-aging process used by larger breweries who use spent bourbon barrels (or Calvados, sherry, and even tequila).
Chips tend to give good flavor within a few weeks (great surface area), while cubes may take several weeks to a few months to fully develop flavors. One mistake not to make is leaving the chips/cubes in the secondary for too long! One of our members put Irish whiskey-soaked chips in a hop sock and placed in a Corny keg to age. However, the keg was set aside for too long and the results were disastrous ...
"Not only did the porter taste astringent and tannic and way too oaky, the chips were in there long enough to most likely cause another round of fermentation from natural organisms in the wood. When I tried to vent the keg, a geyser of porter shot 20 feet across my yard. The rest had to be dumped."
Oak Staves & Spirals
Staves and spirals are not as common, but still readily available from most supply stores. These are generally used for larger batches of beer (10+ gal), and can take months for flavor to develop.
Oak Essence & Oak Powder
Oak essence is a liquid flavoring agent, while oak powder is ... well, powder. Both can be mixed into the secondary (small amounts go a long way!) to give immediate taste. However, just as with any liquid or powder additive/flavoring, the flavors may not seem as genuine as long-term aging with the wood described above.
Source: Raspuzzi, D. Brew Your Own 2014, 20 (1), p. 11.