How to make a gmod server run 24/7?

These usually go with 3 types:
- Web Panel / low-tier (cheapest)
- VPS hosting services / mid-tier (cheap)
- Dedicated server hosting services / high-tier (veryies)

Or, you could set it up on your local computer by port-forwarding, requires a capable router and some knowledge. But, since you said you don't want to keep your computer turned on all day, your only option is to buy a server host.
There are many, just google it up