Find in file: Command-F/Ctrl-F, then to jump to the next match (with the match still selected): Command-G/Ctrl-G to jump to other instances of the identifier under the cursor use Command-[/Ctrl-[ (previous instance) and Command-]/Ctrl-] (next instance).
Zed has no specific find & replace functionality, instead this is realized using multiple cursors:
First search (Command-F/Ctrl-F) for the phrase then press Enter when it's matched OR just select the text you want to find/replace on. Once you have the pattern matched (text selected) that you wantto replace, you add cursors to however many instances of that phrase as you want via Cursor:Multiple:Add At Next Instance Of Identifier, after you start typing, the change will be applied at all selected locations. Running this command many times is not ideal, so to put cursors on all instances in the file at once use Find:All.
Press Command-Shift-F/Ctrl-Shift-F to search inside of a project. Replace in project is not yet supported.