Helping your betta to adapt to its new environment can often be a long process. It will take patience on your part to complete this process with as little stress possible to your fish.
Be near a sink for all of this. I can do any care and cleaning of my betta's tank at just a bathroom sink. Rinse your bowl in warm water without soap, which can poison
fish with even a trace (this means hand soaps, dish soaps, detergents of any type, really any cleaner). Rinse the pebbles and any ornaments also in warm water. Traces of all kinds of things cling to these from manufacture and travel to the pet store.
Place the pebbles in the bowl along with the ornaments. Almost fill the bowl with water from the tap and get it in the range of 70-80F (a broad range of suitable betta temperatures). Condition it (remove all chlorine and chemicals from it) by placing in the dosage that the container tells you. (*Note: in general, I leave the water good and alone for a minute to allow the conditioner to fully take effect.) Also add some aquarium salt as a stress reducer based on the dosages on the package. Float the bag or cup with the betta inside in the water (watch that it does not overflow the bowl. Remove water if it will). This changes the water temperature in the fish's cup very gradually so that he gets used to what the temperature will be like in his new home. Equalizing the temperature can take several minutes to a couple of hours. Test your finger in the cup's water and the bowl water or use a digital thermometer. I personally like using my finger better, since the difference can be felt and not read. The two temperatures do not need to be exactly the same, but the closer they are, the less shocked your betta will be. When if feels about the same, you are ready to place your betta in the bowl.
Typically, it would be very acceptable to place the fish and the water that he is in in the bowl. This first time you should not because the water that he is in is probably quite contaminated (very small amount of water + waste over time = bad water). If at all possible, close the drain of the sink or block it off so that the next step won't end in tragedy. Carefully and gently, pour your fish into the net (obviously, the water will go right through). Now ease him into his new bowl and let him free, pushing the net inside out to get your fish out if necessary. Your betta may be slightly stunned. After all, he has been in a plastic cup for several days, and this water is completely different than what he has been in.
Place the bowl in a safe place that won't be in too much direct sunlight. For the rest of the day, do not feed or disturb your betta. He has undergone a lot of stress and will not be himself for a few days. However tempted you may be, do not feed him or tap on the bowl. Over the next few days, he will become more used to his new environment and his personality will become apparent. The next day you can feed him two pellets (see the Food section for more information on diet). Between five and seven days from now, clean the bowl (see Cleaning).
Further Reading:
Betta behavior, esp. regarding aggression: http://www.bettatalk.com/betta_behavior.htm