Those things are pretty disposable. If it was the cap and/or start windings, I'd expect it to do that every time. I'm thinking more like the bearings are stiff, which warm up after the first run for the day.
But if you still want to open it....
They are all mostly the same. They'll be a screw or 2 in the front panel. One is usually hidden behind the filter. It'll also have several plastic tabs holding it to the metal around the edges. With a small slotted screwdriver, you can work each clip off, and the front panel will fall off.
Then they're be a dozen screws holding the case to the frame. They all come out, and the case lifts up easily.
That's it. Take a garden hose to it, and wash both coils and the garbage out of the bottom. Give it some time to dry before plugging it back in. You will then be able to see the cap, and test it if you want. A hard start kit might help, but they cost a good portion of a new unit. (The main reason why no one wants to fix one.)