I always recommend buying a pair of embroidery scissors for felt crafting. The small, sharp blades make it much easier to cut out small or intricate shapes.
These are the scissors I use in my work - you can see how much smaller the blades are on the two pairs of embroidery scissors compared to the standard sewing scissors.
I always roughly trim any excess felt around the paper pattern piece before I start cutting the shape - I find a small piece of felt is much easier to manoeuvre.
If the shape is really fiddly and/or if you're using a nice colour or some lovely felt you don't want to waste, you might want to practice on some unwanted scraps to get the hang of it before you cut out the shape for real.
Please do share any of your own tips in the comments :)