in order to exploit it from a script running in a web-browser: there's a high-resolution timer in javascript. This one is limited to 5 to 20 us resolution to prevent such attacks.
Recently a shared-memory extension has been proposed. one javascript thread just increments a counter in the shared memory, functioning as a clock for the other thread.
In both cases, (Spectre) attacks can be prevented by browser updates, so any performance impact is not system wide.
This is different from Meltdown, which (only?) affects intel. That one requires kernel changes which cause system-wide performance degradation.