I have a Netgear WNR2000v1 and I was following the instructions from here:
https://forum.archive.openwrt.org/viewtopic.php?id=18279&p=6#p143969
I can telnet into the router, but it says I need to run snarf to download images. How can I do that when the router isn't connected to the Internet? Do I connect it to a switch that's on the Internet and set it to get an IP address via DHCP?
The WNR2000 is a device particularly affected by https://openwrt.org/supported_devices/432_warning, perhaps you find newer and better supported hardware instead.
Yes the way the flash is partitioned in those there is even less usable flash than a typical device with a 4 MB chip. It's going to be very difficult to run recent versions of OpenWrt.
Thanks for the post, but I'd really like to upgrade this device to donate it to a non profit. Buying a new one isn't an option.
Don't take this the wrong way but this is why I dread posting things on boards. It's painful to not get an answer that helps when I'm on a strict budget. 
What about an older version of OpenWRT? I'm open to running something that's out of date. This is for a non profit on a strict budget.
Just a note - if this WERE a newer device, how would I get Internet access using the router's firmware when it's connected directly to the PC via serial or ethernet cable? That's the question I'm asking. 
Connect the WAN port to a LAN port on your existing router that has Internet. By default the stock firmware (as well as OpenWrt) will use DHCP to connect to that network and use it for Internet access. If the existing network uses the same IP range as the LAN on the stock firmware you must change the LAN IP using the stock firmware GUI then re-connect your PC to the new IP.
Thanks! I figured it would be something like that but since there was no mention of it in the steps I wondered if there was something else I missed. Thanks again.
Much appreciated. This is for a non profit with very low level needs (plus it would be fun for me to do just for training myself on this).