There are a few options to dispose of bricks. You can rent a roll off dumpster, hire a junk removal service, sell the bricks to a city or state materials exchange program, or transport them to a landfill or transfer station yourself using a pickup truck.
Renting a dumpster is a good option if you have a lot of bricks and want to budget the cost of removal ahead of time. If you have a smaller number of bricks and do not want to lift the bricks yourself, you can hire a junk removal company to remove them. If you have access to a pickup truck that's big enough to transport bricks, want to save money and only have a small number of bricks, doing it yourself may be a better choice.
Selling bricks via a state or local materials exchange program will help reuse or recycle materials, but it isn't a guaranteed solution; it depends on what is available in your area and if people want them.