The number one reason that users have issues getting their host running is port forwarding. By default, the host is on port :9982. You can see if your host has forwarded its port from this website: http://canyouseeme.org/
If your port is not forwarded, it's probably because your router does not support upnp. Unfortuantely, that means you need to go into the configuration yourself and do it manually. There are some great guides to help you here: https://portforward.com/
Renters know to contact your host from the network address in the host announcement. If your IP address has changed since your announcement, you will need to announce again. If you have a firewall or some networking setup that may be blocking inbound connections from the internet, you need to make sure that it allows traffic to reach the host.
Finally, if you have a dynamic IP address, you should strongly consider setting up something like DynDNS, which allows you to announce a hostname and then manages the dynamic IP address issue for you.
When you run a host, renters form contracts with you. Each time that you make a new contract, you have to put coins into the contract that can be taken away from you if you are a bad host. Depending on how much collateral you are offering, you will have to put up between 5 and 500 coins per contract that you form. You will get all these coins back (and more) if you keep the data that the renter gives to you. And if you lose data, you could end up losing these coins.
The host tracks your current IP address and automatically re-announces every time that the IP address changes. If you have manually set the host's net address (which can be IPv4, IPv6, or a full hostname like myhost.sia.tech), then the host will stop tracking your IP address and instead just use the one you have set manually.
Each host announcement puts a transaction on the blockchain, and incurs a 2.5 SC fee. These announcements are a requirement if you have a constantly changing NetAddress because they are the only way that renter's can discover your new address and download their data. To stop these announcements, you either need to get a static IP address (your ISP can help you with this), or you need a solution like DynDNS.