Hang each of your freshly harvested branches upside down in your drying area. Your drying area should be dark and have a good supply of clean fresh air. Good ventilation is key here. A fan will help, but try not to train it directly on your plants. What you want is air circulating, not blasting at them. Remember to provide lots of space around each individual branch.
Heat will cause your plants to dry faster, but as we explained above, this is not always better. An ambient room temperature should be sufficient. Inspect your plants regularly to see how they are doing and turn them around so that the airflow in the room gets a chance to get to all parts of the buds.
A lot of growers use custom made drying cabinets or boxes. This is basically an enclosed, controlled environment to dry your weed in. Some simple DIY could build you a box with hangers and a throughput of fresh air. You can also buy commercial weed drying cabinets such as this Supherb Drying Cabinet that is suitable for 24 plants.
Drying can take anything from a few days to a couple of weeks. The average time is somewhere around a week. You will know that your plants are dry when branches and stems crack rather than bend between your fingers.
This dried weed is smokeable now, but to get the best of the flavors and potency a final cure is necessary.