There are many methods and techniques of how to teach Algebra.  Whether you are a school teacher, parent, homeschooling family, or a private tutor, the methods that you employ to teach algebra to your students could very well shape their life.

Understanding how to teach algebra in the most approachable way possible can benefit the student in immesurable ways.  For many students, Algebra is the first subject in Math that is very challenging.  If the student succeeds in Algebra, then they will go on into Geometry, Trigonometry, and beyond with the confidence that they will need to succeed.  If they have difficulty in Algebra, the road ahead will be much, much more difficult.

Algebra Teaching Tip #1 - Don't assume your students remember anything. 
When teaching Algebra, you will quickly reach a topic that will require your students to remember and use something that they have learned in the past.  It is very important for the teacher to be aware that it is very likely that the student may not remember these things that they should already know. 

For example, when teaching Algebra you will quickly have problems or equations that involve fractions.  If the teacher assumes that the student is fluent in working with fractions, you may continue ahead with the lesson while the student is still trying to remember how to simplify the fraction.  In this scenario, it would be a good idea to engage your students to determine if they are really "with you" and if they aren't, to back up and review the elementary material a bit before moving on.  It is absolutely critical when teaching Algebra to ensure that your students recall and truly understand the more basic material before you push on to the more complex material.

Algebra Teaching Tip #2 - Tell your students that they can succeed in Algebra.
One may not consider this a directly relavent tip on how to teach Algebra, but in my experience it is a critical step to building the self confidence of the student.  Teachers must remember that most Algebra students have anxiety regarding the subject.  There are a great deal of rules to memorize, new symbols to understand, and terminology that unique to Algebra that the student has not heard before. 

One method of teaching algebra is to begin every lesson with a quick recap of what has been learned recently along with a few words explaining that the Algebra topic of the day is a small extension of what was learned yesterday.  In other words, a minute or two telling the student that today's topic is "not a big deal" can really go a long way towards giving students a confidence boost and open their mind to the Algebra lesson of the day.

Algebra Teaching Tip #3 - Teach your Algebra lesson by working example problems.
Students learn best when examples are presented one by one, with increasing complexity.  The first Algebra example problem that you work should be extremely simple so that every single student in the room will completely follow it.  This builds their confident which will be very important for the remainder of the lesson.

One by one, you increase the difficulty of the Algebra problems that you solve on the board.  It is important not to choose problems that jump ahead in difficulty too far ahead of the previous problem.  If the teacher did this, he or she would lose some students quickly.  By choosing Algebra problems in a gradual progression of complexity, you can hold the student's attention all the way to the end of the lecture, building their confidence along the way.

Algebra Teaching Tip #4 - Show every single step when solving problems
The most important "how to teach algebra" tip is that as the teacher works example problems he or she must never skip any steps.  For example, if you are canceling items in the numerator and denominator of an algebraic fraction, take the time to explain what you are doing.  Another example might be that, when solving an equation, always say out loud and show every step to isolate the variable that you are solving for.  Never assume that because the student has learned this in the past that they completely remember the every concept now.  Reinforcing steps along the way is crucial to being an exceptional Algebra teacher.

To sum up, there are many techniques of how to teach algebra and no one way is the "correct" way.  However, I have found that one of the best approaches is for the Algebra to ease the student's anxiety, along with working a great deal of examples in an ordered sequence that show every single step to get the answer.  This powerful combination of ideas can boost the student's confidence in Algebra, which is the most important element for continued success.