I plug my iPhone into your computer to sync it, but it is not recognized. What should I try first to troubleshoot this?

First, check that the charging cable is properly plugged in at both ends, then try different USB ports or a different cable.

Also, make sure you have the latest version of iTunes, that your computer has the proper drivers, and that the device has internet connectivity if syncing via iCloud.

Finally, force restart both the iPhone and computer as a reset.

See these links:

iOS device not showing in iTunes for Wind… - Apple Community

If your computer doesn't recognize your iPhone or iPad - Apple Support