These little strokers are easy to work on but you need to be systematic when they give you problems. Before you do anything you need to assure yourself that the carb is rebuilt properly and set to factory specs. Make sure the spark plug is the correct one and is gapped properly (always good to have a few set up). White smoke from a 2 stroke is quite normal but it will smell different if it is burning gearbox oil. So with the carb set and spark plugs at the ready you can check the next item; the airbox. I am assuming that the bike has the standard airbox and the filter has been cleaned/replaced and oiled with the correct oil? If not, read no further and get this sorted next. If all of the above is fine you can then move on to checking for air leaks. With the engine running you need to spray around several areas to see if air is being sucked in, the engine note/speed will change as you spray if you have a leak. Using something like WD 40, spray around any rubber part that connects the airbox to the engine so airbox to inlet tube, inlet tube to carb, carb to engine barrel. If when spraying the engine note changed then you will need to sort out where the leak is. The rubbers get hard with time and heat. Ok so we have the carb in spec, some spark plugs in spec, we know the air filter is clean and oiled and we know that there are no air leaks on the inlet side of the engine. Time to tackle the seals. Generally the left seal keeps out air and the right seal keeps out oil. They too get hard and stop doing their job over time and heat. Take off the left crankcase cover (left and right references are with you sitting on the bike ). With the cover off you will normally see the rotor. This will spin with the bike started so, being safe, start the bike. You should see the rotor spinning. Carefully spray some WD 40 behind the rotor whilst listening for a change in engine noise. If there is a change then this seal will need to be changed.
That should keep you busy for a while but make sure you complete the steps because if you just throw the carb back together and it is out of spec or the plug you are using should be for a tractor you will never get the enormous happiness that is riding and smelling a 2 stroke. It is something to be savioured.