You need:
T-shirt
Household thick bleach
Plastic containers
Paintbrush (I have heard to use synthetic brushes instead of natural ones, but most cheap brushes are usually synthetic.)
Tailor's chalk (optional)
A note on t-shirt color:
The colour the bleached part of the t-shirt turns out depends entirely on the t-shirt and what sort of dyes used in the manufacturing process. It's best to use a dark colour, for example black t-shirts normally turn orange or yellow. I've had quite good results with t-shirts from H&M.
Instructions:
1. Wear gloves to protect your hands and tip a tiny bit of bleach into a small container. Find part of the t-shirt that does not show and apply a small line of bleach to make sure it works and see what colour it turns out. Wait about five minutes then wash the test area of the t-shirt.
2. Draw the design on the t-shirt in tailor's chalk if you want, or make a stencil to make it easier to know where to paint (if you use paper it will work fine as long as you don't get bleach on the stencil).
3. Cover the work surface with newspaper to protect it. Put something between the t-shirt to prevent the bleach getting on the back of the t-shirt, a piece of cardboard covered in a plastic bag works well. Put more bleach in the containers, it can be diluted to get different intensities of the colour.
4. Paint the bleach on using a paintbrush, the bleach gets absorbed by the t-shirt so the line will all be the same colour. After a few minutes colour it looks is the colour it will end up, so if it doesn't look bright enough, apply a bit more bleach.
5. When you have finished painting on the design, wait a couple of minutes before washing. Rinse in cold water first, then wash in hot water and detergent. The design will disappear a bit after washing, but once it is dry it goes bright again.