Donning Tzitzit or a Tallit

Since torn tzitzit strings could invalidate the entire tallit (see The Garment and Fringes), the strings of the tzitzit and tallit must be inspected every day before they are worn to ensure that they are still kosher.

During the tzitzit inspection, it is proper to separate and disentangle the individual fringes. Each string is representative of a particular and unique mitzvah, and shouldn't be "entangled" with another.

Tzitzit:

Before performing a mitzvah, we are commanded to recite a blessing, thanking G‑d for sanctifying us with His commandments. The following blessing is recited before putting on the tzitzit:

בָּרוּך אַתָּה ה' אֱ-להֵינוּ מֶלֶך הָעוֹלָם אַשֶׁר קִדְשָנוּ בְּמִצְוֹתָיו וְצִוָנוּ עַל מִצְוַת צִיצִת

Baruch atta Ado-noy Elo-hai-nu Melech ha'olam asher kid-sha-nu b'mitz-vo-tav v'tzi-vanu al mitzvat tzitzit.
[Blessed are you, Lord our G‑d, King of the universe, who has sanctified us with His commandments, and commanded us concerning the mitzvah of tzitzit.]

One who wears a tallit while praying need not recite this blessing. When reciting the blessing on the tallit, he should have in mind that this blessing covers his tzitzit as well.

Tallit:

Before the morning prayers, we put on the tallit before donning the tefillin.

The ideal way to perform the mitzvah of tzitzit is by completely draping oneself in the fringed garment, which is accomplished only through wearing the tallit. A slightly different blessing is recited when putting on the tallit:

בָּרוּך אַתָּה ה' אֱ-להֵינוּ מֶלֶך הָעוֹלָם אַשֶׁר קִדְשָנוּ בְּמִצְוֹתָיו וְצִוָנוּ לְהִתעַטֵף בְּצִיצִת

Baruch atta Ado-noy Elo-hai-nu Melech ha'olam asher kid-sha-nu b'mitz-vo-tav v'tzi-vanu l'hit-atef b'tzitzit.
[Blessed are you, Lord our G‑d, King of the universe, who has sanctified us with His commandments, and commanded us to enwrap ourselves with tzitzit.]

Donning the tallit in four simple steps:

Stand with the folded tallit over the right shoulder, examine the tzitzit…		Then, unfold the tallit and open it wide, kiss its upper edge, and swing it around from the position in which it is held in front of you until it is hanging behind you. At this point begin the blessing.
Gather the two right corners of the tallit, raise them up…		...and place them over the left shoulder; gather the two left corners and bring them up to the left side of the chest. Thus, all four tzitzit are on the left side, two in front and two behind.

During two parts of the morning prayers it is customary to hold the fringes of the tallit in the hands: during the Baruch She'amar and during the Shema. Follow the instructions in your prayer book as to when the fringes are gathered in the hands, and when they are to be kissed and released.