in addition to what redbike says: obviuosly a triple is the best option. however it may mean changing your front mech and shifter, but if you can afford it like i say would be the best option.
Shifters/cables: You wont' need new cable outer, and shifters normally come with inner - however shifters are quite expensive (like 3-figures normally, that said mine are 'out-of-the-back' oem 105s that i got for a bargain £40 a pair new, so hunt around - also try
ebay for second hand ones).
Front mech: a chance that it will 'just work', although it may be the case that triple front mechs have more travel than double ones, so you may need a new one, that said front mechs aren't that dear. (like £20?)
Rear mech: likely need long cage, but try it first with the new setup to see if it shifts ok into all the usable gears.
Rear cassette: with a triple, you may not need to change the cassette aswell to achieve the ratios you need, and if the bike's fairly new then you may not need to change the chain, so therefore could get away with also not changing the cassette.
So, plan: hunt for bargain triple LH shifter, and triple chainset, fit them. Set up existing front mech. If it doesn't work because not enough travel, get triple front mech. Repeat. Check rear cassette shifts onto all usable gears. If rear mech is short cage and is struggling to cope with variation in length of chain, change to long cage, that should be it.
HOWEVER: getting a compact chainset instead of a triple may avoid you having to upgrade to a 3-speed shifter and front mech, if that's important to you and *may* avoid you having to upgrade to long cage rear mech. It will likely take your lowest front chainring down to ~34 instead of ~30, so you may want to go to a 12-27 instead of an 11-23. However so i've heard, with doubles you dont' get as much overlap and are more likely to have to run a small-to-small or large-to-large, resulting in not as good a chainline.