Bandha

Bandha names a technique which works like a valve for Prana (= Energy).

The Yoga philosophy describes Nadis (= energy channel) and Chakras (= energy centres) in the subtle body. So it is clear that Bhanda indicates a very fine technique, only partly achieved by physical action but mainly by pure concentration. There are some different Bandhas for different regulations in the pranic flow. For Ashtanga Vinyasa Yoga this two are most important: Mulabandha and Uddiyana Banda.

Mulabandha

Mulabandha means contracting the pelvic floor.
Mulabandha leads the energy to the lower end of your spine - to Muladhara Chakra.
Mulabandha connects you with earth-energy.
Mulabandha gives you firmness and steadiness.

You can learn Mula Bandha on the one hand by contracting the anus as if you want to stand from going to the toilet, on the other hand by contracting the genital sphincter like inhibiting peeing. The proper position of Mulabandha is just between this two actions. It needs some time to get the necessary awareness of the perineal muscles. So in beginning just contract your anus.
If you need an additional help to get more focus of your perineal muscles use an technique named after Keigel. He invented it for woman after childbirth to tune their pelvic floor again. His training is done while urinating by engaging the perineal muscles to stop the flow of urine and releasing it a view times.

In the beginning it is hard to keep concentration and Mulabandha may waver but with practice you will be able to hold it for your entire Ashtanga Yoga session.

Uddiyana Bandha

Uddiyana Bandha means suck in the lower abdomen by creating an vacuum in your chest while breathing in and out.
Translated wordly Uddiyana Bandha means "flying upward".
Uddiyana Bandha arises the Prana upward in your Spine.
Uddiyana Bandha connects you with air-energy.
Uddiyana Bandha gives you lightness and helps you to come over gravity force.
Uddiyana Bandha also protects your lower back, keeping the spine long and preventing against too much backward bending in the lower back.

To learn Uddyana Bandha you can tag on the following exercise:
Breath completely out and press even the last bit of the air out of your lungs. Place your hands on your knees. Then close your throat while expanding your chest. Just like trying an inhalation but not letting any air in through your throat. Through this method an vacuum in your chest is created an your abdomen will be sucked in deeply. Hold your breath this way for a while trying to get your belly even deeper in and to get more feeling of the action. Before the next inhalation swallow once and release your belly first. If you are completely conformable with this technique you can start and try creating such an vacuum, only slighter, during breathing. Please notice, that absolutely no muscular contraction in the abdomen is needed for this Bandha.

With practice Uddiyana Bandha will become very natural. It just happens more and more all the time during your practice. - Especially when you try to lift your body up in the air.