How do Buddhists use mudras? This is a practice question. I know both Mahayana buddhists and Vajrayana buddhists use mudras. In the former they show up in inconography, and hand resting positions while meditating, in the later it's part of elaborate rituals.

How are mudras used in lay and monastic practice in Mahayana? 

Outside of being a step in larger rituals, how are mudras used in lay and monastic practice in Vajrayana?
In Vajrayana every practice is done on 3 levels - on the level of body, speech and mind. We work with the mind through visualising the Buddha forms, the speech centre is exercised through mantra repetitions and the body - through keeping the posture, using prayer beads (mala) and through the use of mudras.

As a Vajrayana practitioner I can think of a few cases when I use mudras.

First case is while doing the practice of prostrations. A person stands straight and brings their hands together in the 'lotus bud' mudra and places them in the crown of the head, then to the throat and then heart. Then the person kneels down and slides their body on the floor with arms stretched out towards the front. Then hands should meet to form lotus bud mudra again and then the person can stand up to perform another prostration. Touching the head represents purifying the body, touching throat - the speech centre and touching heart - purifying the mind.

People also touch their head, throat and heart centre when standing in front of the Stupa or Buddha statue. When meeting a great teacher or receiving blessing from him people usually hold their hands together and place them on the heart centre. All these gestures signify opening up the mind, speech and body to receive the blessing.

Another example when I use mudras is while attending a recitation of Mandala Offering text. It usually takes place before the teachings or empowerments given by high Lamas. During rituals it is usually the teacher who does the recitation and mudra sequences, however during the Mandala Offering, all students use a special mudra shown on the picture below. One beautiful addition to this mudra is placing rice and flower petals inside the palms and throwing them in the air as soon as the recitation is finished. As for the the meaning of the mudra itself, the arrangement of fingers symbolizes the simplified depiction of the universe one mentally creates and then offers to the Buddha - upright fingers in the middle represent Mount Meru and the 4 pairs around - four continents (if you're interested in details, look here). Mandala Offering is a third part of so-called preliminary practices Ngöndro and it is done to purify attachment, generate merit and create lots of positive impressions in the mind.