How to bottle new brew properly

Yes, one of the best and most common methods is to rack your beer to a secondary fermentation vessel, and an additional transfer before bottling.:

• Make sure primary fermentation is complete first. This is typically several days to a week. You can use a hydrometer to take successive readings to be certain. If the gravity of the beer doesn't change over a couple days, then primary is sufficiently complete.
• Gently rack the beer to your secondary vessel, making sure not to pull traub from the bottom, or floating mass from the surface. I generally leave the beer in secondary for 2+ weeks to settle and mature, but this depends on the style and your goals, and you could shorten the time. More time = more settled.
  • Additionally, at the end of this period you can cold crash the beer by refrigerating the whole fermenter for 1-2 days. The cold temperature will drop the suspended yeast, making it as clear as possible without the use of fining additives or filtration.
• Repeat the racking process a second time to your bottling bucket, leaving the remaining sediment behind. Add your priming sugar dissolved in a few cups of the beer, to the bucket. Mix it well to avoid uneven bottle carbonation, and then bottle. At this point the remaining sediment should be very minimal, possibly invisible.

The only way you're going to prevent sediment from forming at the bottom of your bottles is if you force carbonate (most commonly done through kegging) and fill your bottles after it's been carbonated using something like a counter-pressure filler or a Blichmann Beer Gun.

Your best bet is to follow the instructions you were given. The steps will likely equate to the following:

1. Boil and chill the correct amount of sugar included in the kit.
2. Rack beer out of bucket/carboy into bottling bucket, careful to not oxygenate the beer during transfer. Also, slowly lower the tip of your syphon into the beer while racking it off. Don't simply stick it all the way into the bottom of the vessel. Try to follow the beer-line as to not stir up the sediment in your carboy/bucket.
3. Add the sugar-water solution to the beer and gently stir thoroughly as to make sure the sugar-water is evenly distributed throughout.
4. (I'm assuming you're cleaning & sanitizing everything, therefor omitting it) Attach the racking cane to the bottling bucket.
5. Pour off the beer into the bottles
6. Apply sanitized caps
7. Condition as necessary before consuming
8. When pouring, pour gently to prevent oxygen from bubbling into the bottle as you pour, which will stir up all the yeast and proteins at the bottom of the bottle. Pour off all but the last little bit to keep the sediment in the bottle.

One other thing to note, instructions only take you so far. Yeast is a mysterious, wonderful living organism that has it's own schedule. Just because your instructions say ## days are needed, you'll need to verify that it is in fact ready to bottle. The best way to determine this is to take daily measurements using your hydrometer after fermentation has visibly completed. If the measurements remain the same for three days in a row, you are safe to bottle. If the reading reduces, it is not complete and you need to wait longer until it does steady for three days.

Also, pro-tip: Set your full bottling bucket on the counter over your dish washer and open the door to the washer. 1 - Serves as an awesome bottle rack, and 2 - no cleaning up drips on the floor. Just close the door.