If the speakers are designed to be used with crossovers, I recommend that you use them. I'm assuming that the speakers are the co-axial type with a tweeter mounted to the center of a mid-range cone. Usually such speakers do not come with outboard crossovers and utilize an integrated capacitor to seperate the frequencies. If you do not use the outboard crossover, both the tweeter and the larger cone will be forced to reproduce the same frequencies. resulting in poor sound reproduction. With the crossover, the frequencies will be properly distributed to the speaker components.
To install, connect the + and - factory wires to the inputs on the crossover and then connect the crossover to the speaker. Crossover HF output to speaker HF input, crossover LF output to speaker LF input.
Unless additional wires were included with the speakers, you will have to buy wire to connect the crossover to the speakers. The factory HU wires will only serve to hook up the crossover. I suggest you pick up a spool of twisted speaker wire at your local auto supply store and cut to size after you've determined where to mount the crossover. A site search on "crossover location" or "crossover mount" will provide some ideas. They can be placed anywhere that they will fit between the door and the plastic door panels. Try to get then as close as possible to the speakers and check to see that they don't interfere with window operation. I drilled holes and mounted my crossovers directly to the door with screws, some have used plastic ties through existing holes.