Fill your plant pot up to the brim with a fine soil, such as silt.
Wet the planting soil with fresh water until it is muddy. As mangroves are a marine plant, they thrive in damp growing environments.
Transfer the mangrove seedling into the soil by digging out a small hole with your finger, and inserting the seedling so that its roots are below the surface. Cover the roots back up with soil. The seedling's stem should be all that is sticking out of the soil.
Water the mangrove seedlings with fresh water regularly so that the soil stays damp.
Water the mangrove seedlings with salt water about once a week. This should preferably be ocean water. However, if this is unfeasible, add 2 tsp. of salt to 1 L of water and use that instead.
Once the mangrove seedlings have grown to the size you prefer, they can either be replanted in a saltwater aquarium, or left in their pot. As some types of mangrove can grow quite large, you'll have to transplant them if they outgrow their original pot.