How can I improve my chances to find Hearts (Life Crystals)?
It is particularly dangerous, but if you're really hurting for more health, you could try exploring the dungeon without killing Skeletron (assuming you can't, if you're low on health).
It's reasonably easy to avoid the Skeletron heads that spawn if you continue falling down further into the dungeon - just take out your hammer and head down, breaking any hearts you find until you die. I found a good 3-4 hearts before I was killed, and I wasn't trying very hard to stay alive.
Carry light with you or place torches to make sure that you see the hearts.
Make sure that you explore natural caves; hearts are made with your world and thus don't spawn.
To overcome the depth problem you can explore all depths, which is a point of the digging aspect of the game. Different layers future different things, while I belief the hearts can be found on any layer and perhaps can be found a little more frequent on the lower layers.
If you don't care, a world viewer is a last solution.
There are two suggestions that I have for you, do not read this if you are still in the 'discovery' phase:
So, I would suggest that you start digging a vertical tunnel called a Hellevator and explore natural caves along the way. Another thing you could do is to make a long horizontal tunnel at the Jungle / Lower Dungeon depth; together with Hermes Boots this makes crossing the map easy, instead of having to wait till you ever get those rocket boots...