Quick Summary: You should brush your teeth twice and floss once every day. Search for ADA Seal of Acceptance on dental care products. Mouth wash does not replace brushing and daily usage is not recommended.
Yesterday, as I was brushing my teeth and aimlessly morning-dreaming about the day that lay ahead of me, I realized that I knew shockingly little about dental hygiene. Of course, I was instructed like most others to brush my teeth in the morning and evening by my parents, and told that flossing was probably good too, but I realized that my knowledge was more empirical than scientific. This needed changing, so let’s get right into it.
1. Brushing your Teeth
You should brush your teeth at least twice a day, according to most experts. As with most health concerns, you’re better off asking your personal dentist if you’d benefit from more frequent brushing. Toothbrushes and toothpaste has become commonplace these days, but with such selection in both areas, how can you pick?
When selecting your toothbrush, there are surprisingly quite a few specifics you must consider.
Bristle Softness: Almost every article I read emphasized the importance of buying a soft-bristled brush, since it is most effective at removing plaque and debris from your teeth. [1,2,3] Additionally, hard bristles can result in gum bleeding  and are generally worse at cleaning your mouth than their soft-bristled cousins.
Head Size: Another point of concern is the size of the head of the toothbrush, the part of the brush that is doing the actual cleaning. The main issue here is to match the size of the brush to the size of your mouth; if you have a smaller mouth, you probably shouldn’t go for a larger head size. [1,3] In fact, ImmediaDent even encourages purchasing children’s brushes for abnormally small mouths.
Handle Designs: Although not crucial specifically to your teeth, a bad handle can really ruin your technique. Try selecting a handle that just feels right in your hand; this is more of a personal choice than a definite science. [1,2]
ADA-recommended: Even though most toothbrushes today have the ADA Seal of Acceptance, it’s still a good idea to check and make sure that your selection has it as well. The American Dental Association has definite guidelines before they slap their seal on a toothbrush, requiring manufacturers to use safe components for use in the mouth and maintain quality standards for bristles. 
Electric Brushes: Recently to enter the field are powered toothbrushes that take much of the manual work out of tooth brushing. Both manual and powered toothbrushes are capable of cleaning your teeth well. Electric brushes are recommended for people struggling with their manual toothbrush or that have physical ailments that prevent them from using a traditional toothbrush effectively. Again, this selection is based more on personal preference. [3,4]
Replacement: Most of us are aware of the 3-month suggested lifetime for a toothbrush , but I’ve never been too successful at keeping to that schedule. Basically, if you notice bristles that are not as rigid or straight as they used to be, it’s a good idea to change the toothbrush out.  Colgate also recommends changing after recovering from a cold, since “bristles can collect germs that can lead to reinfection.”
Technique: The way you brush your teeth is more important than what toothpaste or toothbrush you’re using. This is an often-overlooked area that I myself learned the most about, since most of the other suggestions are largely common sense. About.com has an excellent slideshow on technique with images, summarized below: (The ADA has a similar recommendation in this pdf)
- Start in the back, moving clockwise in a circular pattern with the brush at 45 degrees.
- Roll the brush away from the gumline on the outside and inside, ending on the opposite side that you started on. Repeat on your lower molars.
- Flick your toothbrush from the inside front teeth out, both on the upper and lower molars.
- Brush the biting surface of your teeth, starting with your upper molars. Use a circular motion.
- Brush your tongue and inside if your cheeks.
What surprised me was the optional flicking of the toothbrush on your front teeth as well as the suggested length of brushing your tongue and cheeks: 30 seconds. I almost never brush my tongue and I don’t think I’ve ever even tried to brush my cheeks.
You should brush your teeth at least twice a day, in the morning and evening after meals. 
The answer to the selection of toothpaste is actually fairly simple. With the variation in price and manufacturer claims, you’d think that there are wide differences between the effectiveness of individual toothpaste options. But the fact is that most toothpastes perform the same, regardless of what is on the package. 
General Suggestions: In general, as long as your toothpaste contains fluorine, you should be fine. The ADA seal is a good sign as well, since the ADA has guidelines on safety and effectiveness for toothpastes (as it does with toothbrushes).  If you want to whiten your teeth while you brush them, look for carbamide peroxide or hydrogen peroxide.
Check the Further Reading section if you have special needs concerns about sensitive teeth, tartar control, abrasiveness, or dentures.
Flossing and brushing your teeth go hand-in-hand. It makes no difference if you brush first or floss first, as long as you remove the plaque everything is A-ok. The ADA suggests that flossing before may make it easier for fluorine to reach the area between your teeth.  Anyway, much as with toothpaste, your specific brand/type of dental floss doesn’t really matter. In fact, “results from a recent study published in the Journal of Periodontology showed that there was no difference in the plaque-removing ability of four different types of flossing products.” 
General Suggesions: Here, your choice will depend upon personal preference. As with other dental hygienics, you should look for the ADA seal of approval to ensure safety and effectiveness whichever type of dental floss you select. There are a few different types of flosses:
- Electric Floss – This selection makes the most sense for people who have difficulty with traditional flossing techniques, such as older adults.
- Conventional Dental Floss – This is the most common flossing type, where you purchase a string wound up in a small box. “If you decide to use regular dental floss, tear off a piece at least 18 inches long and wind it around your two index fingers. Hold the floss tightly between your index fingers and thumbs and guide the floss softly in between your teeth.” 
- Dental Flosser – This is basically like a toothbrush with a string instead of bristles. Same effectiveness as conventional dental floss, but may be easier to use for some people.
Although flossing technique is does not need as much explanation as brushing, it’s still crucially important you get it right. See a detailed description with images at About.com.
You should floss at least once a day. Usually, people floss before going to sleep. 
3. Mouth Wash
From what I’ve read about mouth washes, there’s not really a consensus about when you should use mouth wash or if it should be a part of your dental hygiene at all. Although mouth wash does not pose health risks , its effectiveness is questionable. Strictly speaking about its ability to increase your dental health, mouth wash is nowhere near as good as flossing or brushing.  You should speak with your individual dental care provider if you could benefit from using mouthwash daily. 
Unlike with flossing or brushing, the ADA does not recommend a specific number of times per day that you should use a mouth wash. 
ADA Resources: The American Dental Association’s website is very clear and well-designed for all dental hygiene concerns: Toothbrushes, Toothpastes, Floss, and Mouthwash.
About.com Dental Product Selection has many suggestions and facts about choosing all kinds of things dental-related.
Toothpaste Selection: if you have special needs, an article over at Delta Dental describes considerations you should take when selecting toothpaste.
 1-800 Dentist: How to Pick a Toothbrush
 Colgate: Choosing the Right Toothbrush
 ImmediaDent: How to Pick a Toothbrush
 ADA: Toothbrushes
 Straight Dope: What’s the best toothpaste?
 Better Homes & Gardens: Choosing a Toothpaste
 About.com: How to Brush Your Teeth- Step By Step Instructions
 Oral-B: Choosing the best dental floss for you
 ADA: Floss & Other Interdental Cleaners
 About.com: Tips for Choosing the right Dental Products
 Wikipedia: Health Risks of Mouthwash
 Know Your Teeth: What are Mouth Rinses?
 ADA: Mouthrinses
 MSN: Open Wide: Your Oral Hygiene