In most cases logging into a library database will look the same as it always has. For example, logging in from the Shared eResources page will lead you to the familiar login screen and then directly to the resource.
In rare cases you will be prompted to select your institution before signing in. Type "TCS" into the search bar and click "KansasCOM, Pacific Oaks, Saybrook, The Chicago School - TCS Education System" (it should be the first option). After that you will be directed to the usual sign-in screen where you will enter your school credentials.
OpenAthens also allows users the option to login directly through the public facing website of a database.