If your dancing is stiff, it is likely because you are using too much tension in your body in the wrong way. When we are novices we try to control each joint, and end up with stiff shoulders, elbows and knees as we attempt to “get it just right”. The effect is more mechanical than controlled. To move naturally you need to find a balance between holding and releasing. To begin with, notice where you are holding tension when you are standing still. Now raise your arms up, and then drop them and let them swing loosely from side to side. Let gravity help your arms swing. This feeling of weight is vital for good dancing.
A useful drill would be to emphasize looseness before control. Listen to a song with a strong feel, and simply allow your body to gently bounce in the knees. Imagine you are playing with the feel as though you are “with” the beat, rather than “on” the beat. Keep your chest soft, and allow your arms to respond to the feel, rather than dictate the feel. This will help your body learn to behave as a whole unit, rather than as a collection of parts. After a minute or two, go back and play the same feel again, but this time with a bit more control, and still maintain the looseness. You will be surprised at how much control you can take away, and still maintain definition.
One of the biggest errors is to just move your limbs and not your core. If the center of the body is dead, the movement will always look unnatural regardless of proper timing. Try to push and pull the movement from the center by thinking of moving your rib cage first, and letting your arms follow. As you step to the side, allow your body to swing to the side a little before taking your foot off the ground. If you are having trouble balancing, take smaller steps and slow down until the movement becomes second nature. Smoothness comes from movement order, not from moving fast.
This can be worked on in just a few minutes a day. First, simply swing to some music, just soft and easy. Sway or bounce to the rhythm, and try to just let the beat go through your body. Next, practice a small bit of choreography at half tempo. Focus on the transitions, not the positions. Finally, dance that same bit full out, once, but with relaxed shoulders and good breath. This way, you will be able to retain some of the softness even when you add more power.
If movements seem strained, pay attention to breathing. Breath-holding is one of the biggest culprits for tenseness, particularly when executing harder phrases. Release the breath on movements which demand more energy (like jumping, strong accents) and breathe in when movements “re-set” or open up. This eliminates unnecessary tension in the body so the movement never stops. Eventually, the breath-movement pairing will produce an apparent relaxation which can’t be faked, even in the most challenging choreography.