It all depends on the size of your instance, but surprisingly little. The most expensive part of running an instance at the moment seems to be users interacting/posting. I’ve had my single user instance running for 22 days, here’s what I have found.
Hardware: I was running it on an HP Chromebox G1 i7-4600U just fine, I did move it to a HP DL360 G7 but this is overkill.
Network: I have 100Mbit/s down and 24Mbit/s up, I can’t even tell when lemmy is federating on my bandwidth charts. It seems to use very minimal network data. Hosting content or users will increase the data requirements, you’d have to get data from larger instances for a perspective there.
Disk: I’m using 4.7G for the postgres and 6.2G for the pictrs after having the instance online for 22 days. This will all depend on how active the communities you subscribe to are. My pictrs is only thumbnails sent during federation, and I have read these purge after some time but haven’t verified these claims.
TLDR; if you have some old hardware around stick a decent sized HDD or SSD in it and you’ll be able to host your own instance for personal use. If you have more users or host images on your instance, the requirements will go up so avoid this if network/disk space is scarce.