Stripping paint from brick is a project most people don't want to tackle. It is time consuming and energy draining, and in most cases very messy. There are a number of ways to do it and some of the methods work better on smooth bricks rather than rough, traditional bricks.
Step 1: Soy Stripper
In these days of 'green' thinking one product you might want to try is a soy based stripper. One name it is sold under is Soy Gel. You need to lay on a good, thick coating of this product and allow it to work. It will stay wet until it works its way through to the bricks below. This could take as long as 24 hours if there is a heavy paint build up. Most likely you will scrape away the first application after you've seen a bit of bubbling up of the paint. If you're lucky and there's only a couple of layers of paint, all you'll need to do after that is wipe the bricks off and you're finished. On a heavy buildup of paint you will have to reapply the gel and wait for it to remove the rest of the paint. Then rub with a wire brush to remove any paint in the cracks. This job is messy but if you want real brick color to show through, you won't mind the mess. Just be sure to cover the surrounding area with a drop cloth so your floors and walls aren't damaged.
Step 2: Paste Stripper
This method involves using a stripping agent then laying a paper like substance over the top to keep it damp while it does its work. The theory is when you pull away the paper all the paint goes with it. It does work on one or two levels and especially well on smooth bricks. On textured bricks you will need to use a wire brush to remove any paint left in the crevices of the bricks. Leave this type of stripper on long enough to allow it to do its work. The tendency is to get curious and start peeling away the paper. Usually double the amount of time stated on the directions is required for proper removal. This product is a bit pricey so you may want to save it as a final resort.
Step 3: Gel Stripper
Gel stripper works in the same way as the soy stripper above, but is easier to find in your local do it yourself or hardware store and isn't as pricey. The advantage of gel is it sticks to vertical surfaces with little or no running. It also takes a long time to dry out and become ineffective so its good on a thick layer of paint and in the cracks and bumps of bricks. Just apply a thick coating per instructions and allow it to work. You can see the paint lift and liquefy. Wipe away all the old paint and use a wire brush to get any remaining paint. Wash the bricks with mineral spirits or paint thinner to clean.