Easiest way to sync audio is to plug the mic into the camera’s external microphone jack.
Use a lavalier (tieclip) mic. It can be hard-wired, or you can use a wireless microphone. A wireless substitutes a small belt-pack transmitter and a receiver on the camera for the mic cable.
If you don’t want to use a wired mic, and can’t afford a wireless (good ones start at about $500), then you can use a minidisc recorder that has a mic input, or an iRiver iFP-7xx or -8xx series MP3 player. Plug a lavalier mic into either unit and record the audio. In post, dump it into the computer and sync it up with the video by sliding the clip until the audio matches the audio from your on-board mic.
For most of your audio needs, try https://www.bhphotovideo.com or other reputable equipment dealers.
Regards,
Doug Graham