You can buy the canvases and paint from all good art shops - I recommend Ken Bromley Art Supplies if you're in the UK. A great place for art brushes is Rosemary & Co who make brushes by hand (they're cheaper than you'd expect and you'll find the service and quality are second to none).
I start by painting each canvas in the required colour using a good quality acrylic paint. Acrylics are better for this than emulsions (but you can use emulsion test pots or leftovers to save money or match a room) because they give a much longer-lasting finish, won't go brittle and they come in an amazing array of colours. One tube goes a long way.
One of the big problems is how to dry them when you've painted the edges too - the paint will stick to shelves and mark them and newspaper just makes a mess on the back of the canvas. I save metal lids from jars to raise them from the surface - and the paint doesn't stick easily to the metal lids (doesn't matter much if it does) but you do have an area of bare wood on the back of most canvases, which helps.
Your next step is painting a second coat. Don't try to save time and put just one thick coat on rather than two thinner ones - it's just not worth it, as the finish won't be nearly as good.
Once the first two coats are completely dry and you're happy with the finish, you can add letters. I do these freehand, but I know not everyone is up for that! You can print large letters out on the computer in your favourite font (try a few different ones) and cut them out to use as stencils. You can draw round them with a pencil, or transfer them using tracing paper. There's a really good tutorial here which shows how to transfer letters from the computer (lovely idea for a big garden sign too!).
You'll need two coats on each letter too. My letters are a neutral cream, which works well against brights or pastels. You can see from this photo below why you need two coats - some of the letter is painted twice and the rest only once and you can tell the difference.
The spotty letters are popular - and to make the spots I stencil circles onto the letters. I used to do this freehand, but it was time-consuming getting those circles looking right! You'll notice there are very few full circles and they're arranged to look quite random but I pop them fairly evenly around both sides of each letter, alternating the sides.
OK, you've guessed it. Each spot gets two coats too. You'll need a fairly small brush for this, and a steady hand too.
Once the dots are done and dry, you might want to neaten the backs of the canvases. Hand painted canvases often look a bit messy on the back, which is actually OK, but you might prefer to give them a coat of paint to neaten up.
And there you go. A lovely set of canvases to brighten up your child's bedroom wall.