The function Search returns a table, which you can bind to a property that expect table values, such as the Items property in a gallery. In your case, you need to add a control that has one of such inputs (e.g., gallery, dropdown) to display the items filtered by the search term.
PowerApps currently does not have a control that, while you're typing, will search some data source and suggest entries (i.e., an auto-complete text input control) - feel free to create a new suggestion in the PowerApps Ideas board for that.
An alternative which I've seen used is to use a pair of controls - a text input and a gallery below it that displays the matches from your data source. For an example, take a look at the app below:
The gallery Items property is set to the following:
SortByColumns(Search(PulpFiction, TextInput1.Text, "Actor", "Character"), "Actor")
So as the user types in the text input, the items presented in the gallery are updated. You can then set the OnSelect property in the item inside the gallery to take an action based on the selected item (for example, navigating to a different page).
