In general, going long is buying, and going short is selling. A long position will increase in value if market prices increase.
For example, in Forex trading, going long is buying the trade currency of the Forex currency pair. If you were going long on USDJPY, you would be buying USD by selling JPY.
For securities, going long is taking ownership of a security through buying it, as opposed to going short where you sell the security without owning it.