There certainly is!
Its called "acclimating", and its super important. The reason you do it is because if the fish is suddenly placed into a tank that has a different temperature or different water parameters (or just different water), it can go into shock! Shock can make it feel sick, sluggish, or even kill it or weaken it. :'(
What you should do for not only the first time you add the fish, but every water change:
Put the fish in the cup it came in with whatever tank water is in the tank. If you dont have the cup, use a sandwhich bag.
Put the fish in a safe spot. Make sure it cant jump away and can get air.
Change out the water, keeping the temps as close to what they were before as possible. (Ex. The water was 77'F, use new water that's 77'F) You'll need a thermometer. If its a few degrees off, 76-78'F, no biggie. If its 70'F, it needs warmer water or needs time to heat up from a heater.
Add conditioner to your water.
Now, let your betta "bob" for 5 minutes. If its in a cup, dont let the cup tip! It could drown. Same for the baggie. For the baggie, either clip the betta to the side with a clothes pin or fold the top of the baggie over itself, which will keep it afloat.
After 5 minutes, add in a bit of the new tank's water. Not too much, not too little. :) This will help with the temp. difference as well as the water one.
After 5 more minutes, do it again.
And again, 5 minutes later!
I wouldnt do less than 10 minutes, 15-20+is perfect.
After that time, carefully and gently remove as much of the old water from the fish's baggie or cup. Make sure the fish wont come out!
Then, gently coax the fish back into the big tank. Try to get as little old water into the nice, clean tank as is possible.
Let the little guy relax, since that's a big deal! lol!