[HIPPO]

There is a thread here called "one cylinder FLHT" by Rustler. Read it.

As a side comment the plug wires on these bikes become pretty suspect after a year or two (if they are OEM wires) so it couldn't hurt to change them anyway together with the plugs.
Check the basics, compression/leakdown, spark and fuel (intake gasket leak) and take it from there.

 

[HIPPO]

If the bike has been sitting for a long time it is quite likely that the fuel system is gummed up, in particular the carb guts and petcock screen or injectors if the bike is EFI.

 

[HIPPO]

Good looking bike. Ideally you would disassemble the carb totally and dip it in one of those carb cleaner buckets they sell at auto stores, you don't need the 5 gallon ones, they have little 1 gallon ones or smaller for 10 bucks or so. Make absolutely sure you remove all rubber and plastic components before dipping. If the diaphragms look tired might as well replace them.