The make up of the mitzvos
The mitzvos are split into two groups: positive and negative mitzvos. The larger part is negative mitzvos – 365 in total while the positive mitzvos total 248. Together they form 613 mitzvos, known as “taryag” that is the numerical number in hebrew letters – תרי”ג. This is seen in the Torah that was given to the Jews on Har Sinai, where the numerical equivalent of the word “Torah“, תור”ה, is 611 mitzvos plus the two first commandments that we heard directly from Hashem, total 613. The significance of the this goes much deeper. An example, is that the Vilna Gaon points out that in Megillas Rus, that we read on Shavuous the time of Matan Torah, the hebrew word רות has the numerical equivalent of 606 plus the the seven mitzvos that all people (who by definition are Bnei Noach) need to keep totals 613 mitzvos!
Understanding the difference between the 248 positive and 365 negative mitzvos
These type of mitzvos are understood since they are called positive this means that it requires the person to do actively do something. However, what does it mean to do a negative mitzva? Surely this means inaction? Why then does the person get rewarded for doing nothing? The answer must be again that a person DOES do something but finding himself in a situation where he is drawn to doing a sin and instead he controls himself and does not do the sin. This lack of doing the tempting sin is what it means by negative mitzvos.
Different types within mitzvos
The mitzvos are not all identical in how they are done. Some require simply machshova, thought, to fulfil the mitzva – examples being pigul or noisor. Others require speech, like nedorim and shevuous, but the main bulk require action, like eating matza or building a sukka. This is how the Torah tells us to do the mitzva. Nevertheless, there is always different levels on how to do each mitzva. An analogy being how eager a young student wanting to please his teacher will do his bidding as opposed to a an older bored student. Each will follow the same instructions but the effort and level to how they do the task will vary greatly. The same applies in what goes into doing a mitzva.
Have to and optional mitzvos
Certain mitzvos we must do while others are conditional. We must love and fear Hashem, these are essential mitzvos, known as “mitzva chiyuvis” – obligatory mitzvos. Other mitzvos are optional, known as “mitzva kiyumis“. This means that when we find ourselves in a certain situation, only then must we do the mitzva. For example, if we want to eat kosher meat we now enter a situation where we will be required to do the positive mitzva of shechita, slaughtering. Putting up a mezuza is only when one is living in a room and requiring tzitzis is only when we wear a four cornered garment.
Mitzvos on the person or outside them
There is also a category of mitzvos known as “mitzva shebikufoi“, mitzvos that need to be done by the person. An example is bris mila, putting on tefillin and tzitzis and not wearing kilayim. There is a also a category called “mitzvos hateluyois boeretz“, mitzvos that are dependent on being in Eretz Yisroel. These include the mitzvos of termuois and micerous as well as shemitta.