Users working with data don't impact the data reading portion of the backup. They can impact the log, as noted above, but that's mostly depending on the amount of logging done.

As far as the timing, that can impact backup since you have I/O and CPU resources being shared among all processes. If the backup runs at the same time as something else doing work on the server, there is an impact, but it's never been that significant for most of my servers unless heave compression is in use.

The ways you speed up backups are compression (needs more CPU, reduces I/O) and backup to faster or multiple devices.