Connect your speakers to the stereo amplifier using the speaker cables. Some speakers use 1/4-inch jacks and plugs, while others use bare stereo wires that must be attached with clips. Some speakers are self-powered and don't need an amplifier.
Connect the mixer to the stereo amplifier using the RCA cables. Connect the red and black leads to the red and black jacks, respectively. If your speakers are self-powered, plug them directly into your mixer, plugging the left speaker into the left side plug and the right speaker into the right side plug. Self-powered speakers generally have 1/4-inch plugs; use 1/8-inch adapters if your mixer only has 1/8-inch inputs.
Connect the left turntable to the left channel on the mixer by plugging its RCA cable into the phono input jacks on the mixer. Plug the red and black plugs into the corresponding jack. Attach the ground wire to the mixer using the "ground" screw. Repeat the process with the right turntable and the right channel of the mixer. If you are using CD decks, the process is the same, except you don't need to attach ground wires. If you are using both CDs and vinyl, connect the turntables to the phono jacks and the CD players to the "line in" inputs.
Attach the power cables to the mixer and the stereo amplifier. Plug everything in.