Friction shifting is dead simple. Start by cleaning and lightly lubricating all pivots, springs etc on the dérailleur and shifter, and ensuring that any cable guides are clean from dirt and debris. You don't want any rust, especially on the friction surfaces, otherwise it won't be smooth at all. Get to work with some wire wool or fine grit sand paper and get everything nice and shiny again.
Get those parts attached to your bike again, and reassemble with new decent quality gear cables, again lightly lubricated, and cut to the appropriate length. Assuming the old cables were the correct length, you can use those as a guide. You want to avoid any tight turns in the cable, whilst ensuring it isn't excessively long.
When fitting the cable ensure that the chain is on both smallest cogs (front and rear), and that the shifters are pushed all the way forward (so none of their travel is used). When locking the cable in to place on the dérailleur ensure that there isn't any excess slack in the cable. You can adjust out small amounts of slack with barrel adjusters if present.
Once the cable pinch bolt is tightened down and everything is locked in to place, just set the limits on your dérailleurs, set the friction on the shifters to your preference (tight enough that the gears don't auto change under pressure, but not too tight that you can't shift smoothly), and you're pretty much done!
