Rather than running a Tor relay, running a simple Tor bridge (e.g. via the browser add-on Snowflake as suggested by @ryokimball@infosec.pub) is probably the best thing to do with one’s home hardware.

Actual relays must suffice certain requirements, according to the Tor project:

Requirements for Tor relays depend on the type of relay and the bandwidth they provide. ==== Bandwidth and Connections ====

A non-exit relay should be able to handle at least 7000 concurrent connections. This can overwhelm consumer-level routers. If you run the Tor relay from a server (virtual or dedicated) in a data center you will be fine. If you run it behind a consumer-level router at home you will have to try and see if your home router can handle it or if it starts failing. Fast exit relays (>=100 Mbit/s) usually have to handle a lot more concurrent connections (>100k).

It is recommended that a relay have at least 16 Mbit/s (Mbps) upload bandwidth and 16 Mbit/s (Mbps) download bandwidth available for Tor. More is better. The minimum requirements for a relay are 10 Mbit/s (Mbps). If you have less than 10 Mbit/s but at least 1 Mbit/s we recommend you run a [/wiki/doc/PluggableTransports/obfs4proxy bridge with obfs4 support]. If you do not know your bandwidth you can use http://beta.speedtest.net/ to measure it.

As for exit relays aka exit nodes, the obligatory advice is of course to not run them at all unless you know exactly what you are doing both legally and technically, and probably only if you’re a foundation or something.