I am assuming you are doing an extract batch with some steeping grains (Crystal, Chocolate, etc), and not mashing.
I understand you boil for 15 to 20 minutes and add the grain.
No. Grains should never be boiled. Even if you are just steeping or mashing. Grains should be added to approximately 155 F water (150 to 160 F). Steep for 15 to 20 minutes, raise the temperature to 170 F, and remove the grains. If the grains are in a strainer bag (paint bag from hardware store) that makes it easy to remove. If they are loose, you can use a strainer and swirl it around the water/wort to remove most of them; don't worry about small bits left ..... but you will when you get more experienced.
Bring the water to a boil and add the extract. It can be added before you get to boiling. Be careful not to scorch the extract on the bottom of the pan.
You then boil again for 30 minutes and then add some hops and keep boiling for 30 more minutes and add the rest of the hops.
Bring to the boil, boil for 10 minutes and then add the bittering hops. Add the rest of the hops per the recipe.
I then stir may want to stir the wort for a few minutes and let cool.
I then add the wort to my fermenter along with water to reach 5 gallons.
I add my yeast.
No need to stir at the end unless it is to get the last of the hops in suspension. Cool as quick as you can. Use ice water in the sink. Keep the lid on the pot all the while when it is cooling. Add to fermenter, top up with water and add yeast.
(HERE is a QUESTION: I am not sure how to use the hydrometer? Do I use it at this point in time? and how do I know what the reading should be?)
After 10 days to 14 days I should be ready to bottle. (QUESTION: I have to add sugar at this point. Do I add it right to the beer or another container?)
Now I am ready to bottle and let sit for a couple weeks.
2 questions I have are in orange. Also, did I miss any major steps besides the obvious...Steralize?
Don't concern yourself with the hydrometer at the moment. It won't make the beer taste any different. Assume the starting gravity is as noted in the kit.
Depending on the yeast, fermentation temperature it may be done in 10 to 14 days. I usually leave mine at least a month. After 10 days, take a sample and heck the gravity with the hydrometer. Drink the sample, don't put it back. If the gravity reading stays the same for 3 days, it is done. It will improve if you leave it longer, but you can bottle at this point.
To bottle, rack to the bottling bucket/container. Always dissolve the priming sugar in water (boil to sanitize), add the sugar to the whole batch in the bucket and gently stir to mix. Then bottle.
I don't think you have missed anything major.
Good luck.