Put on some merengue music--the Resources section contains a link to a good example.
Listen for the "marching" beat inside the merengue music. This beat is often kept by the drum, but various instruments may share in maintaining the beat.
Take small steps in place as if you were marching. Stand up straight and let your hips shift and rock naturally from side to side with the motion of each step. You're dancing the merengue.
Listen for the steady 1-2-3-4 beat in the bachata music. You don't need to worry about fast or slow steps--just listen for the steady beat and practice counting it.
Start by putting your left foot out to the left a short distance. This happens on the first beat of bachata music. If your step is so wide that you have trouble keeping your balance or making the next steps fast enough to keep up with the bachata music, take a smaller step next time.
Bring your right foot in toward the left on the second count of the bachata music, then move your left foot back out to the left on the third beat of music.
Bring your right foot in toward the left on the fourth and final beat of the rhythm pattern, but don't touch it down yet. Instead, rock your hips to the right in time with the fourth beat of the bachata music, like a small, gentle "hip bump," a la disco dancing, then put your foot down.
Repeat the pattern in the other direction: Right foot out, left foot together, right foot out again, left foot in and bump. Then reverse back to the left. Continue dancing back and forth with small steps. This is the basic bachata step.
Spend a lot of time listening to salsa music and, if possible, watching people dance to it. Music videos are a good way to do both at the same time, as salsa singers usually dance to the rhythm. See the Resources section for a link to a salsa music video example.
Practice the basic salsa step once you have a feel for the general rhythm of the salsa. As with the bachata, it functions on a simple 1-2-3-4 beat. The pattern given will be for the man; the woman dances as his mirror image, so that when his left foot is moving forward her right foot is moving back, and so on.
Take a small step forward with your left foot, and rock your weight onto your left foot, to beat one of the music. This is called a rock step. It's OK for your right foot to come off the floor just a little bit as you do this. On beat two, rock your weight back on to your right foot.
Bring your left foot back to the middle for beat three and shift your weight onto it, freeing your right foot up to take the next step. Pause on beat four. If you have trouble pausing, you can tap your right foot in place on beat four instead.
Do the same pattern in the opposite direction with your right foot: Rock step back on beat one, rock back to the middle on beat two, bring your right foot back to middle and shift your weight on beat three. Pause on beat four. Now repeat the entire pattern, starting with the rock step forward with your left foot on beat one of the salsa music. This is the basic salsa step.