If your TV has only a single composite (yellow/red/white) AV input, you cannot plug both devices in simultaneously without a switch or converter. Here are the practical solutions, ranked by quality and convenience.
Buy a manual composite AV switch box ($10–$20). Plug Wii and DVD player into the switch inputs; run one output cable to the TV. Press a button to toggle sources. No power required for passive models.
Many early HDTVs have component (YPbPr) inputs (red/green/blue video + red/white audio) plus one composite input. Use official Wii component cables for 480p on component; keep DVD on composite.
Avoid: Cheap "Y-splitter" cables merging two outputs into one input — they cause signal collision and potential hardware damage.