How does looking at the tzitzit/fringes remind us of G-d’s commands? Perhaps the illustration above, based on Rashi, explains it:
שמנין גמטריא של ציצית שש מאות ושמנה חטין וחמשה קשרים הרי תרי”ג
“The tzitzit will remind one of all the mitzvot because the gematria (numerical value) of the Hebrew letters of the word “tzitzit” is 600, and there are 8 threads and 5 knots in the fringes, so that you have 613, which is also the number of mitzvot in Torah.” 
Rashi’s comment is itself based on a baraita: “This mitzvah is equal to all the other mitzvot together.” 
Why does Torah command us to not only wear tzitzit, but to look at them (אותו/literally, at “it”) and remember God’s commands?
Because a spiritual truth needs to be reinforced in order to become an integral part of our thinking.
Ordinarily, our minds are overwhelmed by the impressions and information provided by the senses. Beyond this, our minds are flooded by our own thoughts, feelings and urges.
Spirituality reality is beyond the realm of thoughts and senses. At the same time, all of our mental activity takes place within Spiritual reality; it’s our perception, not reality, that’s limited.
The exit from Egypt and the giving of Torah testify to the presence of a Spiritual reality that is involved in our lives moment-to-moment.
But we forget.
Under the pressure of daily life, we become so immersed in the details that we lose sight of the all-encompassing reality. Even if we attend synagogue on Shabbat — or every day for that matter — what do we find ourselves thinking about once we have gone back “out into the world?” Our minds are filled with concern, with worry, with fear, with anger, and so on.
God, in Torah, tells us to use the senses for a spiritual purpose:
Look at the tzitzit.
Remember the commandments.
Know that God is as Present to you today as at Sinai.
Do this repeatedly during every day.
The same could be said of a mezuzah: It’s a reminder. But only if we use it as one.
The Hebrew also says [‘Look at’] “אותו.” It can mean “it,” taking “tzitzit” as singular, but it can also mean “Him” — i.e. Look at “Him;” at God.
King David says, “I have placed [Sh’vi’ti] God before me always.” 
On this, the Baal Shem Tov said:
“[Sh’vi’ti] is related to ‘hishtavut’ (equanimity). No matter what happens, whether people praise me or shame me…it is all the same to me…[because] it comes from God.” 
The Rambam tells us that God’s existence is the basis of everything else that exists.
In truth, there is no “else.”
Let us, then look at everything and always remember God.
 © 2010 by Rabbi Eli Mallon. All rights preserved. Do not use, copy, or reproduce without written permission.
 Bamidbar/Numbers 15:39
 Rashi on Bamidbar/Numbers 15:39. Thanks to Rabbi D. Linzer for the citation. Note that in order for “tzitzit” to equal “400,” Rashi has to add a second “yud,” as the Hebrew of Torah spells it [ציצת] — i.e. with one “yud.” Without his doing that, the gematria would equal “390” instead of “400.” He does it without adding a consonant (thereby changing the root) by elongating the second vowel, necessitating the additional “yud.” He then counts the “yud” as a consonant equal to “10,” even though, strictly speaking, it’s functioning here as part of a vowel:
“Hiriq (חִירִיק) is a Hebrew vowel sign represented by a dot [“.”] underneath the letter. In modern Hebrew, it indicates the phoneme…”ee”…[A] Hiriq is often promoted to Hiriq Male (חִירִיק מָלֵא) [for grammatical reasons]…A Hiriq Male is a Yud [“י”] preceded by a letter with a hiriq [“.”] and in writing without niqqudot/vowels, the hiriq is omitted, leaving only the Yud [“י”]…” http://en.wikipedia.org/wiki/Hiriq
 Menachot 43b
 Tehillim/Psalms 16:8
 Tz’va’at Ha-Rivash/Testament of the Baal Shem Tov, no. 2