Place the paint on a paper plate - if you have more than 1 toddler or older kids as well I find it much easier to provide each child with their own paper plate with paints to avoid arguments.
Using a paint brush, paint designs on the eggs. To avoid smudging you can paint half and allow to dry.
Once your toddler has finished painting then place the egg in an egg cup to dry.
If you have used acrylic paint then skip the next step and use the eggs to decorate your home for Easter. When dry if you have used washable paints for kids then paint over with some PVA glue or Mod Podge.