Routing Algorithms and Hosts
I believe you are talking about the Internet and the IP. Here are answers of your questions: 

First note the internet is a network of networks. Networks communicate with each other through routers. These big networks are like the ISP, your university or a big organization. Your computer belong to a small network in your ISP subnetwork. This small network is probably your WiFi switch and your computer. 


Do hosts find themselves in the routing tables ? NO, but from the IP address of the host and its subnetwork, a router can tell whether they belong to the same subnetwork or not. If they do belong, then there is no need to route the message to another router. The message is simple sent down the subnetwork. You have to study in this case the BGP protocol and the structure of IP. 
Your host got nothing to do with routing. The ISP takes care of all that. or your cellular company if you are using your mobile phone .. or etc .. It would be hugely complicated to let these terminals take care of that. Again, you must have a look on the IP structure. 
If you try to send a message to X, then your router will look at X (which has an address probably similar to 122.23.12.11 or whatever !) from the upper digits, the router (which is your ISP router in this case) will know which neighbor router to send it to. In general, Internet routing is greedy. How a router selects its neighbors ? [that's another topic]


One advice: dont look to the Internet from a pure theoretical point-of-view.

I guess I answered your question ?