Just head out and walk through the pedestrian zone to the sea, then either turn left for the beach or right for the marina.
Puerto Mogán is divided into three little areas:
The beach area is the newest and has the cheapest bars and restaurants, the banks and ATMs and the Spar supermarket (the cheapest in town). The highlight is the golden beach itself and the row of bars and restaurants next to it. Walk to the far end of the beach for views of the Mogán cliffs (this is a great snorkelling spot too).
To get to the marina area, walk back along the beach and over one of the bridges. The marina and all the famous colourful houses, bougainvillea arches and canals is right there. There's nothing to do except wander, look at the boats and the fish and pick a place for your first meal. If you feel like really stretching your legs, walk through the boatyard and all the way to the end of the harbour wall. The bar at the end has great views of the whole of Puerto Mogán.
The village area of Puerto Mogán clings to the steep hillside just behind the marina. It's a higgledy piggledy maze of steep lanes and white houses with a viewpoint at the top (tricky to find but worth the search).
For the cheapest supplies head to the Spar supermarket on the beach side of the canal. Just follow the canal back and you can't miss it.
As for things to do in Mogán, there's the Yellow Submarine, a handicraft market on Mondays, a huge Friday street market and several boat trips leaving from the marina. Bus links to other resorts are frequent but the little ferries are much more fun.