I have a full node(Parity) running at home. I know I can trust this node. How would I go about connecting to it from another computer?
geth and having rpc enabled on your node you can:
geth attach --rpc=http://your_ip:your_port
Or, using the MIST wallet, you can connect to it
yarn dev:electron --rpc http://your_ip:your_host
Or, using web3.js, you can connect to it from your code like:
web3 = new Web3(new Web3.providers.HttpProvider("http://your_ip:your_port"));