I'm looking at different VORs on a sectional chart and I see the frequencies but I also see a channel number associated with them as well. What are these channel numbers and how do you use them?
They are DME (TACAN) channels. If you look close the the VORs, you'll see that they are either a VOR/DME or a VORTAC station. DME is the distance portion of a TACAN. When added to a VOR, you have a VOR/DME. If a complete TACAN is co-located with the VOR it is identified as a VORTAC.
The military uses TACAN. If you were to have a TACAN receiver, you wuold tune it using the channel number.
DME is available to civilian users with a DME receiver. The DME channels are paired to VOR/ILS/VHF frequencies (It's a multi-page table in the DME standards.) For convenience, DME receivers are tuned using the paired frequency.
When you tune a VOR or ILS, that frequency is also sent to the DME automatically tuning it to the proper channel. They are channels because DME actually uses two frequencies, one for transmit and one for reply.
So, to answer the question: unless you have a TACAN receiver, you don't do anything with the channel number. They are on the chart for reference.