Carby's are fairly simple to overhaul - as long as you take your time and note where bits come from so they go back in the right place.
Possible problems for your description - check in this order
Fuel filter blocked/dirty
Tank strainer dirty
Sometimes there is a small strainer in the "banjo" where the fuel pipe connects to the carby (above the needle and seat for the float)
Main jet in the carby blocked (most likely the problem) but most work to check.

Regulated compressed air is almost essential for cleaning out a carby, but an aerosol tin of carby cleaner or crc will do.