I've read a lot of these suggestions and most are very good.
The most important thing to do is to understand what you are doing. So this doesn't mean one time through your reloading instructions. Reloading is almost as much fun as shooting but far more important safety wise.
After you understand what each step does then make a your own instructions in order of what you need to follow.
The first step is to inspect your brass. Make sure its all the same caliber and not damaged.
Then determine if the brass needs to be cleaned. I don't tumble my brass very often. Something I learned in benchrest shooting is all those guys use a sizing die wax in place of oil or grease. Its much cleaner and faster, and does a much better job. In addition after you have sized them you take a clean rag; I use mechanics shop rages, wipe each one by turning the brass inside of the rag. You'll be ammazed at what this does, it cleans and polishes the brass almost like new. As for the inside its not that important. So now size the brass. You'll have to check the papers with your dies for setting up your dies.
Now inspect each piece under a good light to make sure you have no split necks or spilts in the body of the brass. Also check the case mouth and primer pocket.
Next step if you aren't using boat tails is to use a neck expander die so you can seat the bullet without smashing the lip of the brass.
Clean and inspect your primer pockets. I use carbide primer pocket uniformers. It keeps the primer pockets clean and very uniform. At some place down the road you will understand how important this is to not only safety but accuracy as well.
Next is to prime each case. The best way is to use a priming tool as they seat each primer to the best uniformity, but also will not crush the primer, plus its very fast. I keep my primers in a small metal box with a hinge on the lid, and make sure you mark the box for what kind of primer it is. When done priming take your fingue and feel the primer seating for any that don't feel right. Your fingers are able to deteck variations as small as .002"-.003"
Now you have your brass prepared, this is the most time consuming part of reloading. Next get your reloading book in front of you and make sure you are looking at the right caliber bullet and load data and the correct powder. As everyone else has said before always start out below the recommended load, but be sure to read all load instructions first as some bullet loads have also listed that you can not go below a certain charge. The reason is you can get secondary ignition which creates very high pressures, dangerous to you and your rifle.
Next is to charge the brass, maing sure again you are using correct load data, powder and following all instructions. Always , always look at the inside of your brass and make sure you have not doubled the charge in any of the brass, nor have you missed any. Well seasoned loaders have done this so don't take it lightly. You have to do the charge inspection under decent lights. I have nothing but flouresents in my loading shop, safer in my opion.
Now seat your bullet with caution making sure it is ligned up with the throat of the brass. Pay attention to OAL (overall length) start long and then slowly adjust your die to the die desired length. If I am loading for a brand new gun/caliber I will seat bullets in a few dumy rounds (no powder or primer) and then chamber them, making sure they feed right and the bolt cloases all the way without any unusual pressure. Then pull the loaded round out and check the OAL of your seated bullet/round. If its shorter then required, you may want to reconsider seating the bullets further into the case. Another big danger of having ammo too long is if you extract a loaded round you may leave the bullet in the throat of your gun and dump powder all over inside your chamber and trigger, makes a real mess. If this aver happens to you your first priorty is to remove the bullet in the rifle. If you fail to get the bullet out and fire anotheer behind it you will have whats called a squib round and an exploision, your gun will be damaged, maybe ruined, and you could lose your eyes or your life. I had a squib round when goose hunting a few years back and the barrel ruptured. I was lucky as my injuries were only moderate. This was shooting factory ammo by the way so not my fault.
A hand full of years ago a man shooting at a Nationly sanctioned benchrest shoot had a live round in his chamber after the official called for cease fire, so he had to remove the live round and left the ram rod in the barrrel to retrieve the bullet he knocked out and inspect the chamber for powder. He ended up leaving the rod in the barrrel and lost his life when he began firing again. Saftey and keeping your mind on what you are doing is always worth the time and effort.
From here your next objective before going any further is to make sure your OAL is correct and the bullets are seating properly.
After this you can continue to tweak your load for best accuracy, not fastest speed. Its a real advantage to have a chronometer, maybe borrow one from your buddy and invite him over and the both of you can work up loads.
Always record all data. Brass, powder, primers, OAL and of course accuracy. For testing accuracy always fire 3 shot groups. Measure your groups and record the size.
One more rather obvious precaution is no smoking. I know I may have forgotten something so compare this list to the others.