The photos above illustrate the power of even basic photo editing programs. The original image is on the left, the edited version on the right. Granted, inserting the sky goes beyond the scope of a first step. However, the major improvements were attained by using basic tools such as cropping, saturation, brightness, contrast, etc.
Getting Started
The hardest part of photo editing is taking the initial step. None of the information presented here will do you any good if you don't go to Amazon, ebay, Cost Captain (if you have a student ID), etc. and purchase an editing program.
Programs
When it comes to selecting editing programs, the short answer is it doesn't really matter. The basic tool bars are similar from program to program. It is important to realize though that even the relatively basic programs are so powerful that it is unlikely that you will even use a small portion of their capability. Do NOT go out and purchase a several hundred dollar editing program. Not only do you not need it, the extra complexity will bog you down and impede your learning progress.
Also, earlier editions of programs, even used ones on ebay, are absolutely adequate. I've seen Paint Shop X on Amazon for $30 or $40. You can get lightly used Adobe Photoshop programs on ebay, 'buy it now' for $15 or $20.
Over the years I've accumulated three common editing programs. I like all of them for different reasons.
ArcSoft Photo Studio 5.5
This program used to come free with the Canon Rebels. It has far fewer capabilities than the 'big boys' and yet I use it the most. Why? It is nimble and simple. While it lacks capability, the most commonly used tool bars are exceptionally easy to use. I find myself doing the majority of my work with ArcSoft and then polishing off the more sophisticated stuff with the more powerful programs. If you do buy ArcSoft Photo Studio you will eventually need to augment it with a more powerful program.
Corel Paint Shop Pro X.
Readily available. Cheap. Fairly simple to use. Very powerful. Excellent perspective correction and distortion correction tools. As with the Adobe program the only downside is that its power is a double edged sword in that the expanded tool bars may be a little daunting for a first timer. If you can't find Arc Soft Photo Studio this would be my recommendation. There is also an excellent book on how to use the program 'Paint Shop Pro X for Photographers' by McMahon.
Adobe Photoshop Elements
This is the Microsoft of the editing field. Its the most commonly used program and you can find lightly used copies for just a few dollars. Its powerful and can handle anything you could throw out to it. The clone stamp is excellent. I prefer the Paint Shop Pro's perspective correction tool over that of the Adobe product. I picked up a lightly used copy of version 2.0 for $15 on ebay and even this early version does more than I'll ever need.
In summary, you can get very powerful programs for less than the cost of a freight car so don't research (aka procrastinate) BUY.
THE LEARNING PROCESS CAN NOT START UNTIL YOU PURCHASE AN EDITING PROGRAM. DO IT. THEY ARE CHEAP!
Most Used Clean-up Steps/Hierarchy
I think what intimidates many people initially when faced with an editing program is the sheer magnitude of the capabilities. You open the program up and are faced with a huge menu of tools. Where do you start? Fortunately, the vast majority of your work involves using just a few of the basic tools over and over. Learn the basics and you will be off and running. Once you have the basics down you can fill in the gaps in your knowledge over time. The most common problems you are likely to encounter in your day to day shooting are: underexposed shots, images that are muddy, dull, and lifeless (particularly when shooting indoors), and finally shots where the color is off (too blue, red, green, etc).
Crop: Cropping is simply cutting away extraneous parts of the image to feature the subject more prominently. You may find that floors, ceilings, pavement, etc. comprise a fairly large portion of your picture. Simply cutting these away can make a dramatic difference in the quality of the photo.
Auto Enhance/Quick Fix: Most editing programs have this feature. Always try this first as in almost half the cases they will do all the clean up you need. If not, hit the undo button and try other measures.
Saturation: Saturation refers to the brilliance of your colors. Particularly with indoor shots you may notice your photos lack vitality. Bumping the saturation up slightly can recover your colors. The problem with saturation is many people employ too much of a good thing. Don't overuse this tool to the point where your colors are unrealistic.
Color Balance: Particularly with indoor shots you may notice your photos are a little too blue, red, or green. Most programs employ simple sliders to correct for this. You can see your results as you move the slider so color correction goes very quickly.
Brightness vs. Tone Adjustment: Under exposed photos are a common problem. The brightness tool lightens the entire image up across the board. If you need more control, the tone adjustment tool will allow you to brighten or darken certain ranges while minimizing (but not eliminating) the impact on other ranges.
Contrast: Dull lifeless images can often be improved by a slight bump in contrast. Don't over do it though.
Sharpness: A gentle bump in sharpness can improve your results. Again, a little goes a long way. Use the 'sharpen lightly' tool or 'unsharp mask' tool.
The steps above are just a tiny sliver of the capabilities of even the most basic editing programs. You will find, however, that they are all you need to get your photos where you want them to be. The nice thing about digital is the instant feedback/quick learning curve. Take a test photo and play around with the tools above to get the hang of them. For more important photos ALWAYS back up your image and do your editing on your copy. If you don't backup and make an editing error you have no way of recovering the original photo.
Re-sizing
Two big reasons image size are important are disk storage space and internet etiquette. Imagine this, you sit down at your computer to retrieve an important email for work. Your email program gags for what seems like an eternity as it tries to download a series of massive files. The file content - a dozen gigantic photo images of Aunt Millie's new cat, each sized at 2MB. Had Aunt Millie been up on her internet etiquette she would have known to resize her photos to a more manageable and polite small file size for emails. Another example, you've been in the field on a photo safari shooting various rail side signs. Is it necessary that each of the 200 photos you shot that day be 3000 pixels across? No.
In general you need large images for: magazine publication, critical photos that you will need to be able to blow up to view detail, your most important family photos. Everything else can be stored at a smaller file size. There is no reason to use up computer hard drive space on run of the mill pictures. Since you won't know ahead of time which photos are important, shoot them all large and then downsize most of them via editing. As a rough rule of thumb an image that is 1000 pixels up or down is more than adequate for general use. All editors have an image resize tool. If you are consistently emailing your friends routine photos over 1MB they will likely be less than pleased.
Note: Think of a photo as a sheet of graph paper made up of a grid of squares. Photos are the same concept with each 'square' being a pixel. If your sheet is 100 squares across and 100 squares down then you have a 100x100 pixel image. A Canon Rebel set on 'Large' will take images that are over 3,000 pixels (or squares) across and 3,000 squares down. Again, pixels are the number of squares. The "volume" of data in a photo is measured in KB or MB just the same as any other document you are used to working with, MS Word for example. All things being equal (meaning same file format) more pixels means more volume and thus a larger file size.
Back up
With digital photography hard copy paper printouts of images are becoming a rarity. Backing up your images becomes critical and yet it is so easy to put it off. Losing a rare rail image is bad enough, losing the perfect picture of a family member would be heart breaking. External hard drives are relatively cheap. As a minimum, back-up your most important images on the external drive. For really important photos I put copies on disks and mail them to friends or relatives for safekeeping. Having copies at a second site provides further protection in the case of fire or flood. I suggest doing the same for your home movies.