Changing Crankset on a bicycle
You've got two basic problems: namely the spacing of the rear dropouts, and the style of the dropouts. You've got a smaller problem of the chainline.

If (and only if) your frame is steel, you can respace the frame. Otherwise, you're limited to hubs that fit within the existing frame spacing. Given I assume your bike has rear facing horizontal ("track") dropouts your best bet would be an internal hub. Shimano make/made a number of 3-speed hubs that fit 120mm track spacing (on hubs this is called the over-locknut distance or OLD.

Assuming the bike doesn't have cable eyelets, adding a front derailleur is much harder. You need something for the cable outer to provide a reaction force against, else the cable will have no tension. Cheaper vintage bikes used to have clamp on cable hangers, but I've not seen anything like this for sale.

Be aware that whatever you decide to do, this is potentially a very big/expensive project. You may well be better off with a second hand vintage 10-speed.