How can I sync my iPod with two computers?

The answer depends on a few factors: 1. The generation of iPod you are rocking 2. If it's music only you are concerned about, or if other media is involved. The answer gets a lot more involved when pics & video come into play. 3. If the music is all iTunes-purchased or if it's a mixture of CD ripped / iTunes-purchased. iTunes-purchased music can be transferred to a different computer after you authorize your work PC as one of the 5 machines you can authorize to play your purchased content. I believe this process will also work for TV shows & Video but I haven't needed to transfer non-music content to a different machine myself. The command in iTunes is File -> Transfer Purchases from "_____", with your iPod name filled in  the blank. I was able to transfer music files from a 3rd Gen iPod to a Mac or PC via the command line, but this is a more involved solution than what you may need so I'll leave it to a follow-up answer if you need it.

"Manually manage" may be a better solution for you, rather than syncing which is technically different. However even if you deactivate syncing on both computers as described in Apple's support article, that still leaves you unable to copy new material onto the device from more than one computer. There are other websites that have instructions on how to convince the iDevice that the two different computers are actually the same, so you can copy songs on from each one. Quora may not want this information published but if you search the web you'll find it on sites such as Lifehacker or MakeUseOf I think.