You don't need any special machine or drying varnish to dry your finger and toenails quickly after painting them! I learnt a really useful and easy method off my friend and I now use it every time :)
The secret to drying your manicures is water! Nail varnish, like oil, doesn't mix with water and instead of making your nails wet, it helps to dry them! After painting your nails, fill a small bowl with cold water. The colder the better. Then put your hands (or feet) in the water and keep them there for as long as you can before you freeze to death. The first time I did it I was worried that the nail varnish would come off in the water, but it doesn't. Then rest your hands on a towel or gently wipe them until your skin is dry. By this time your nails should be dry too!
This method has always worked really well for me. Apparently if you add nail varnish remover to the water then it dries even quicker, but I don't want to try it in case it goes wrong! I hope this helps :)