Why is pradakṣiṇā done clockwise?

so that the deity always stays on your right — the side of respect — as you walk around with God at the centre.

The word pradakṣiṇā comes from dakṣiṇa, which means “right”. Walking clockwise keeps the deity on your right-hand side throughout, and in Indian culture the right side is the side of honour; we also keep respected elders and sacred fires on our right. The deeper meaning is simple: just as the planets circle the Sun, our life should revolve around God at its centre.

An odd number of rounds — one, three, five or more — is common, and many people walk slowly while chanting a name or mantra. In Śiva temples, many traditions do only a half round: devotees go up to the channel (somasūtra) through which the abhiṣeka water flows out, and turn back without crossing it. Some temples have a large outer path for a full circuit around the whole complex.

If the space is too crowded or you cannot walk, turning around once on the spot with folded hands is an accepted substitute.

Source: Āgama tradition; common practice · Śiva temples: half round

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