There are a few facts about how evolution happens in Picbreeder that can help you evolve better images.
It's important to realize that the "DNA" in Picbreeder is designed to become more complex as more generations pass. That means that early on in a lineage, your best bet is to produce simple things. As you go along, images will naturally become more interesting, because the DNA actually expands as it evolves.
However, if you branch from an image that has already been evolved for a while, you get more advanced complexity right away. So if you want to start seeing a lot of detail right away, look for a good image from which to branch, either from yourself or from another user.
A funny thing about complex images is that while they may change a lot when you spawn a new generation, often they have a way of morphing into something that's still very interesting! Be on the lookout for these kinds of really interesting transformations. Everyone benefits when you publish something that represents a whole new kind of idea.
Because images can sometimes transform, it's possible to go from one type of image to another. For this reason, it is not always necessary to find exactly the right thing to start from. In particular, look for regularities in the image that you might want. For example, is it symmetric? If you want symmetry, even if the image is not something you like, it might be a good starting point.
To be a good breeder it helps to think about how things can be related. For example:
If you think in this way, you can see how many things are reachable in a whole new way.
Finally, because complexity is designed to increase over generations, the longer a lineage becomes, the more novel discoveries become possible. So it's a good idea to spend some time working on long lineages (either your own or someone else's) to bring them even farther along the path of discovery.
Because Picbreeder is a community of explorers, what you are doing as an individual user is not just finding new images, but creating new paths from which others may embark. By participating in this process, you are helping to make possible more than what you have done alone.