I installed Trust Wallet on my Android smartphone. I carefully wrote down the reminder words in the proper order and hid them. I know where they are. How do I use the words to get the key (public or private) for receiving bitcoins into the wallet from, say, Coinbase?
The idea behind a seed mnemonic phrase is to provide a readable format for the seed. It is mostly used for backup purposes. Let's say you lost your phone. You'll be able to recover your bitcoin wallet based on the word list you have saved in a secure place. Also the Trust Wallet may stop being available as an app at some point, and the seed will allow you to restore the backup in another software wallet if you know your derivation paths.
How do I use the words to get the key (public or private) for receiving bitcoins?
First of all, you don't need the private key to receive bitcoin. If someone asks you for your seed or private key - be aware it is probably a scam. There are ways of using the seed to set up a watch-only wallet - based on xpub derivation which Trust Wallet doesn't provide (it's an extremely basic bitcoin wallet).
But you'll see your bitcoin address when clicking on the bitcoin logo in the Trust Wallet app and then going into the "receive" tab. Trust Wallet will create a set of keys automatically based on the seed and will show you just the one address for deposit.