https://www.homebrewtalk.com/f35/bottling-tips-homebrewer-94812/
The above link was the method I used when I was bottling. I made a dip tube from the curved part of a clear plastic racking cane and stuck it into the stopper that was originally for the airlock in the lid of the bucket. Then inserted the stopper into the spout from the inside - worked great.
To remove labels from bottles and clean them, I soak them in a solution of OxiClean or PBW. OxiClean is cheaper but seems to leave a white film on the inside of the bottles sometimes, whereas PBW doesn't (at least with my tap water). A vinegar rinse should remove the film. After cleaning and rinsing the bottles thoroughly (I rinse with a jet bottle sprayer which connects to a adapter screwed into my faucet), I hang them on my bottling tree to dry overnight. On bottling day I sanitize using a Vinator pump with StarSan and again hang them on the bottling tree. I sanitize a few bottles, then let them drip a bit while I fill a few bottles, then sanitize a few more and fill the ones I had previously sanitized, etc. This way the bottles are still wet with StarSan when I fill them, so still sanitized.
The first thing I would do is move my carboy up onto a table to give it time for any disturbed trub to settle out before racking to the bottle bucket. Then I would boil a couple of cups of distilled water and dissolve my priming sugar into it, then cover and let it cool while I sanitized everything.
To sanitize, I mix up a gallon of StarSan (use distilled or RO water so it will not turn cloudy and become ineffective quickly). I keep the StarSan in a 1 gallon glass jug and put some into a spray bottle. Also I mix up a couple of gallons of Iodophor in 1 gallon water jugs. One gallon of Iodophor goes into a large shallow plastic tray I use to sanitize my gear - I like this better than a bucket because I can completely submerse my autosiphon in the tray. Into the tray I put all small parts to be sanitized - autosiphon, bottling wand bucket spout, dip tube and stopper, siphon hose, the short piece of tubing that I use to connect my bottling wand to the spout (as in the link above), etc. I pour some Iodophor or StarSan into the bucket and swish it around to sanitize the bucket, then put the spout onto the bucket and the dip tube and stopper into the spout. Assemble the siphoning tube onto the autosiphon. Then pour the extra gallon of Iodophor into the bucket, swish it around, and run some out through the spout. Then I use the autosiphon to pump some of this out of the bucket and down the drain just to make sure the autosiphon is thoroughly sanitized. Put the autosiphon/tube assembly back in the tray of sanitizer, invert the bucket to drain, and be SURE the spout is closed (don't ask me why I emphasize this). I like to cover the spout with some sanitized plastic wrap secured with a rubber band.
So now, put the bucket on the floor with the carboy on the table just above it. Pour your cooled priming solution into the bucket (gently, so as not to aerate it). Put the autosiphon into the carboy (make sure the little black cap is on the tip of the autosiphon) and the end of the siphon tube down in the bottom of the bucket. Hold the bottom of the autosiphon about midway in the carboy and pump it to start the siphon. As the liquid drains from the carboy, lower the autosiphon to follow it. Watch the beer in the siphon tube - you can see when you begin sucking up yeast as the beer in the tube will turn cloudy. When this happens, stop siphoning by just raising the bottom of the autosiphon out of the beer. Remove the autosiphon from the carboy - it is a good idea to have an empty bucket ready to drop it into to avoid dripping all over the floor. At this point I always used a long sanitized spoon to give the beer in the bucket a very gentle stir - just a couple of stirs, but be careful not to aerate the beer - you just want to make sure the priming sugar is well mixed. I'm sure a lot of people don't do this for fear of oxidizing the beer, but I always do.
Now loosely cover the bucket with the sanitized lid and lift it up onto the table, or onto an overturned bucket or kettle on the table per the link above. Attach the bottling wand to the spout with the short piece of tubing (use hose clamps if needed, but I never needed them), spray the wand with StarSan and open the spout on the bucket - the plunger at the end of the wand should prevent leaking. You should have your caps in a bowl of sanitizer. Sanitize a few bottles (Vinator or just dunk into sanitizer and drain) and commence filling. I like to fill all the bottles and place the sanitized cap loosely on top and cap them all later. But if there are two people, one can bottle while the other caps.
Good luck. It's really pretty simple once you get started.