I have a small collection of Bionicle elements that I would like to incorporate into my System builds but I am a little unsure how to use them.
What are the different ways to use these two types of bricks together?
since the bionicle-pieces only have holes for technic-connections and no studs to use then directly with bricks, you'll have two possibilities:
I'd prefer the first option - it's easy, more robust, not controversial and just need two or three pieces in most cases. for example a brick with axle-hole and a small axle or a brick with hole and a simple peg is all you need to get started.
As oezi says, Bionicle elements are usually compatible with Technic connections only, but there are quite a lot of system bricks which have Technic connections as well.
As for what to do with Bionicle elements, only your own imagination can answer that. Once you've an idea about what a specific Bionicle element is going to represent in your creation, how to connect it is usually not the biggest issue. So, go surprise us!
Of course, some green Bionicle elements are best used in wilderness, as they have "wild" shapes — allowing you a little more freedom than if you wanted to build buildings. Giant weapons on the other hand may become a cool building decoration.
The best example I can think of is this palmtree which is just brilliant.