Adding new fish or mobile inverts to reef/marine aquariums!

To begin with, the new life needs to acclimatize to the tanks parameters like salinity, oxygen level, KH, temperature, PH and so on!
If acclimatising is not done correctly then the PH on the fishes gills will not match the PH of your water affectively causing potentially serious harm to your new tank life's breathing capacity in the coming days or even possible eye damage.

Once you have matched the water in the bag or your bucket to the tanks water, set up a small net or plastic container with holes in it made with a soldering iron, drilling makes the holes with sharp edges.
With a net, add a weight in it like a stone and the net is hung in your tanks water, whether it be in your sump or tank, it doesn't mater, it is the same water.

The netting has holes of course, as does the container to allow flow through keeping oxygenated water to the that new life form till ready to release it into your tank.

At roughly 15 to 20 minutes before lights out, you feed your after tank life as usual before adding new fish, wait a minute or two now add the new tank life.
If added after lights out, it may get harmed by corals or anemones or panic due to no time to find a hiding spot.
If added too early, other tank life may attack them due to territorial issues.
Rule of thumb- when they sleep together, with out fighting to begin with, they usually have the best chance of acceptance by lights on!

If not fully trusting of LFS water
Make sure the water your new tank life came in, from the LFS, has no contaminants like parasite cures in that water, if it does, then just take water from your tank to the container and take out the same amount from your container/bag gradually and throw that water away till you are happy with the time frame, then put new life into holding net or container for release.

This way is if LFS water is of good quality.
Once you have acclimatised the new life in a container for maybe 30 minutes to an hour, "or longer if you wish", by passing small amounts from the tank water to the container, then the same amount back to the tank keeping the container at the same amount of water as you do this, then the new life is ready for your tanks water.

Make sure you keep moving water to the container or oxygen in that container/bag will deplete to a critical level and harm your new life form.