Turn off the lights on your aquarium and try and keep the room you are acclimating in dim as well. This will help prevent any undue stress on your new arrivals after they're removed from a dark environment.
Before opening the bags, float them in your tank for 15 minutes to allow the temperature to equalize.
Open the bags and roll the edges over to trap some air and allow the bags to float. You may also remove the critter from the bag and place it into a bowl or other container to acclimate it there. If you do this you will have to ensure the temperature does not fall during acclimation.
Place a half cup (quarter cup for smaller bags) of your tank water into each bag. Repeat this step about every 5 minutes or so to allow the water conditions in the bag to match the conditions on your tank.
Once the bag is full, empty half of the water out and repeat step four until the bag fills again.
Net your critter from the bag and tank it.
Discard the water left in the shipping bag.
Extra Information
Always acclimate your critters no matter if they appear dead in the bag. Often times they may be lethargic due to shipping stress and conditions in the bag and will often come around in no time
Leave the aquarium lights off for most of the day if not the rest of the day. This help any fish you have received find a comfortable spot in your tank while keeping from being harrassed by the established inhabitants. If you are keeping very territorial fish, you might also want to try moving around some of the rock work to break up territories causing all the fish to regroup at the same time. This can help level the playing field.
Critters which you receive shipped damp will not need acclimation after being floated for the temperature equalization. Simply open the bag and place them in the tank.
Do not leave turbo/astrea snails on their backs. They can not right themselves and will quickly starve and die.
Inverts such as stars and snails are very sensitive to changes in specific gravity. These may require a longer acclimation period.
I keep fish and corals in the same system here. I never use medications and I do not cut corners by keeping the SG low in my systems. The specific gravity is kept as close to 1.025 at all times as possible. I am confident in my water conditions, but due to the chemical processes which take place inside shipping bags, you may not want to place the water into your own tank.
Please do not rush the acclimation. Your critter is depending on it to remain healthy.