All you need are a few inexpensive bottles of acrylic paint, a canvas, brush and something flat to mix colours. All 4 of these acrylics cost me a grand total of $4.
Start with a bit of the original colour in a small container. Paint your first (or last, depending on whether you want to ombre from dark to light or light to dark) letter. Add a bit of white to the container, mix and paint your next letter. Take a bit of that colour and add it to your paint palette in case you need to touch up the letters. Continue adding white and painting your letters.
Work quickly because acrylic dries fast.