How do I find my frame rate (in FPS) in Skyrim?

Unfortunately, Skyrim does not provide a method for displaying its FPS to the player. The console command tdt (ToggleDebugText) was expected to work by many players, as it did in previous Bethesda games. It doesn't work in Skyrim, though, so third-party software really is your only choice in this case.

I've used FRAPS successfully with Skyrim, the free version is sufficient for just an FPS readout.

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In general, if a game or its engine doesn't specifically provide an implementation of an FPS readout (usually via some sort of console command or similar), then additional software is your only choice.

You can use the Elys MemInfo SKSE plugin to display FPS along with several other useful statistics in-game. This will likely result in more accurate readings and is simpler than using a separate tool.

Requirements:

Skyrim version 1.1.21 or above is required.

Skyrim Script Extender version 1.1 or above.

At least Windows XP SP1.

Installing:

Extract the content of this archive into your Skyrim folder. ( by default the folder is "C:\Program Files (x86)\Steam\SteamApps\common\skyrim" )

If correctly extracted you should find SKSE_Elys_MemInfo.dll inside your "\DATA\SKSE\Plugins\"

Usage:

Hit Scroll Lock in-game, direct gaze toward the top right corner of the screen.

Steam has an in-game FPS counter for any game built into the in-game settings.
From HowToGeek:

In Steam (while no games are running), just head to Steam > Settings > In-Game and then pick a position for the FPS display from the “In-game FPS counter” dropdown. Look at the corner of the screen you chose while playing a game and you'll see the FPS counter.