If you read my Press Selection Guide and chose Use Case Number 1 these are your next steps. Also see the Brass Cleaning Guide.

I'll assume you have bought a Lee Precision Breech Lock Challenger Kit and a 4 Die kit from Lee. This guide will help you reload any pistol calibre and most straight wall rifle cartridges.

You will want a sturdy desk or workbench to bolt the press to. I built a simple bench from 2x4's and plywood. Another option I have used is to bolt the press to a 12" piece of 2x4 and then use a clamp to hold it in place.

You will need reloading components now. We need brass, primers, powder, and bullets.

There is a lot of load data available. The data below are my preferences.

9mm: Brass should be pretty easy to find. The best place to find it is at your feet after shooting commercial ammo.
CCI or Federal small pistol primers will work great. The Federal's are softer and work great in guns with light springs.
Titegroup is my favorite powder for 9mm. Other options are Accurate Arms #5, VihtaVuori N320 and many more.
AIM Projectiles, Canadian BDX, and CanPro are good options for projectiles.

40S&W: Same as 9mm, except powder. You'll want HS6 or Autocomp.

45 ACP: Same as 9mm, except you'll want large pistol primers.
Edit: Thanks to Anthony for the email. There is some 45 ACP brass that takes small pistol primers instead of large primers. These should be sorted out and placed to the side. This brass can be used when large primers are unavailable, or at a match when you won't get the brass back.

38 Special: Same as 9mm, mostly. Some may want lead projectiles like wadcutters or semi-wadcutters. There are other powders options, I like Winchester WST with wadcutters.

44 Mag. or 44 Special: Coming Soon

45/70: Coming Soon

Let's start preparing some brass. The instructions that come with the dies are excellent, so start by setting up the sizing/deprime die. Run at least 100 through and we'll work with these.

Setup the hand priming tool. Use the appropriate shell holder, and use the tray to flip all the primers so they are facing up. I've never had a primer go off in the priming tool, but it is possible. Wear eye protection, and hold the tool so that the top of the brass is pointed away from you.

Set up the powder expander die. This die will bell the case slightly so that the bullet can be placed on for seating. (We skip this step for rifle cartridges). This die also allows us to fill the case with powder. The Lee dies come with a scoop and some load data for using the scoop. This can be handy when you are not too particular about the powder charge. You can also buy a set of scoops for finer tuning. The alternative is to use the powder measure. Take your time to go over the load data and figure out which powder you want to use, and how much. There will be another article soon on fine tuning loads, but to begin, start at the minimum charge, and work your way up to where you want the load.

Here are a couple of quick examples that I have come across.
Loading 9mm for IPSC:
Minor power factor is 125. Power factor is bullet weight in grains multiplied by velocity in feet per second then divided by 1000 to make the number more readable. If I have a 125gr bullet, I need it to travel 1000fps to make 125 power factor. In reality I want to see 1050 to 1080 feet per second because I don't want factors beyond my control to cause the power factor to fall below 125.
I picked Titegroup for the powder, so a rough guess from the load data says I need to start around 4.0 grains. So I would load 20-50 rounds, and then go to the range and fire them over a Chronograph to measure the speed in fps. Depending on my results I would add or subtract powder to get the velocities I want.
Loading 45/70 for fun:
45/70 is a fun rifle round and great for hunting medium to large game in North America. There is a lot of load data for 45/70 depending on the firearm you are using. I was loading for a Marlin Guide Gun. I started with the "lever action" data and picked the minimum load. The rounds gave quite a punch into the shoulder, and while they may be great for hunting, they were less than fun to shoot. Adjusting the load data down and changing powders produced a load that was fun to shoot and still had enough power to be effective while hunting.

Set up the bullet seating die: Use the load data to figure out the overall length you want. Some firearms prefer different seating depths. If you are having feeding issues from the magazine, experiment with the length.

Some bullet seating dies have a built-in crimp. For the most part, a separate crimp die is the way to go. But if want to save some time loading, feel free to experiment with the crimp. I've found that using the bullet die crimp can destroy brass that is not sized perfectly, and can cause little to no crimp on a case that may be sized a bit too small.

The Lee Factory Crimp die is the best way to finish off a case, especially if you are shooting a semi-automatic. If the crimp is not proper, then the recoil of the gun can cause the rounds in the magazine to change their overall length. Bullets can be pressed into the case riding up the feed ramp also. The factory crimp die reaches down the bottom of the case and can do a better job of reducing the bulge at the bottom of the case that can form sometimes.

Reloading Data:

Hodgdon IMR and Winchester Data

Accurate Arms

VihtaVouri Handgun Data

VihtaVouri Rifle Data