The primer isn't what does the glueing. Technically the bond you're creating when joining PVC is very similar to working with acrylic as the cement actually melts the PVC so that when it dries you wind up with one piece. The primer is an etchant/degreaser that removes all the dirt, oil, and ink and etches the surfaces to be joined so that the cement will more readily absorb into the PVC and melt it properly. Clean the outer diameter of the pipe and the inside of the fitting with the primer and let it dry (read the bottle). Don't touch the primered surfaces as the oils in your skin can get where you just cleaned. Then take the cement and apply it liberally to the outside of the pipe, then to the inside of the fitting, then once more to the outside of the pipe and join the pieces while twisting a quarter turn. hold the pieces together for 20-30 seconds so they don't come back apart. That's how you're "supposed" to do it according to the cement/primer instructions. IMO, I'd listen to them before anyone else since it is their product... In my personal experience, I've never used primer on anything for my tank, although had I known about the clear primer I probably would have. BUT, I've never had one single leak from a cemented fitting, and I probably have 20-30 of them. For pipe 2" or larger as stated above, you really should use the primer.
One last think, make sure you're using the proper cement/primer combinations for the type of pipe you're using and what you're cementing it to. The general purpose stuff is fine for regular white schedule 40, but if you're going to cement it to acrylic or some other plastic, there's a kind of weld-on that is much better. Just read the bottles and you'll be fine.
Oh, and keep a window open with a fan or do it outside. The fumes are nasty (and flamable from what I've read).