FYI, not that it's a problem: 53/39 is a standard double, not a compact. A standard double won't give you the hill-climbing gears you'd get with the smaller chainrings on a compact double or a triple.

I think your bike's currently got a Shimano FC-1057 crankset, which is square taper. An Allen key will take the bolt/dustcap off, and if it's not a self-extractor, then you'll need a crank arm remover to pull the crank arms. I'd suggest a Park Tool CWP-7 because it'll work on your old square taper crankset as well as Octalink cranks.

I think I see splines on the bottom bracket behind the crank spider. If that's the case, you'll need a Shimano-compatible splined bottom bracket tool like a Park Tool BBT-22 or BBT-32. Again, like the crank puller, these particular tools will work with your old square taper parts as well as Octalink so you can use these bottom bracket tools to install (and remove) your new crankset.