Mostly people will use a q-tip or similar to remove any tonsil stone that the can see. But this can be a bit painful and you can damage the tonsil if you use to much force. There is also a chance of a slight soreness after you used a q-tip.
Another way is to use something called a waterpik to remove your tonsil stones. This way is more hygiene as it's only water that gets in contact with the tonsil. You remove the risk of infecting the tonsils with foreign bacteria ass well.
A waterpik is a device that was designed to help to floss the area between the teeth with water. The result was great because it did the job better than traditional flossing threads and picks.
It works by flushing water through a mouth piece almost like the ones that you can find at the dentist. You can regulate the water pressure manually if you need more or less power for any object that's stuck.
How do you use this waterpik to remove tonsillitis?
It's very easy as you use it just like you would use it normally. Stand over the sink and open your mouth and begin to flush the tonsils with the waterpik. Angle the mouthpiece so that you target the tonsil crypts (Where the tonsil stones are) and flush them out. This is were the adjustable water pressure is good. If you have a stone that doesn't seem to come out the simply raise the water pressure and it will surely pop out.
This is also a good preventive method as well. If you flush out your tonsil crypts regularly then you won't have so much trouble with these stones.