Hello Avehkala
The 1st thing to do is to decide if you can solder new capacitors in place of the old ones which have dried out or become leaky. Don’t power the unit up anymore until this is done, and check the fuse, should be rated for no more than about 1 amp.

If you’ve never soldered wire before, practice by fixing a couple of cheaper radios. Watch some videos. Post your general location if you need help local assistance.
There is a big can on top of the chassis that contains I think 4 polarized electrolytic capacitors.
They should be replaced either by restuffing the can or by mounting them on a new terminal strip under the chassis, leaving the old can in place but disconnected. If an old capacitor develops a short, it can cause overheating of the power transformer.

With new caps installed in the power supply, your Fisher can be gently powered up and should work again. Some of the smaller caps may be faulty but the tuner should be safe to test. Monitor the power transformer and other components for overheating. Always have a load, speakers, dummy resistor or amp, connected when operating a tube device.

Measure voltages to ensure it’s back to correct levels and if so, enjoy your Fisher!