CLI:

If you are using the CLI you ought to perform the following steps:

Download the new binaries from here. Extract the new binaries to a new directory of your liking. Copy over the wallet files from the old directory (the one that contains the v0.11.0.0 binaries).

Note that a blockchain resync is not needed. If you open monerod-v.0.11.1.0 it simply picks up where it left off.

GUI:

If you are using the GUI you ought to perform the following steps:

Download the new binaries from here. Extract the new binaries to a new directory of your liking. Open monero-wallet-gui ^1. It should automatically load your "old" wallet.