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One is to precede the left side with regards to tying clothing. Thus all clothing that have laces which are required to be tied on two different sides, left and right, one is to precede the tying of the left side to the tying of the right side. [Thus if one has sleeves of a shirt that need to be tied he is to first tie the left sleeve and then the right sleeve. The same law would apply by pants that have laces on each end of the leg.]
Is one to button his left sleeve prior to his right sleeve?
Some Poskim write that the above law of preceding the tying of the left side applies by all forms of ties and not just to strings. Accordingly one is to button his left sleeve prior to his right sleeve.
 Basra 2/4
Other Opinions: Some Poskim rule that the giving of precedence to the left when it comes to tying only applies to shoes, however when tying other clothing one is to precede the right side. [M”B 2/6 in name of Artzos Chaim 2/4]
The following Poskim rule like Admur that by all clothing the left precedes by tying: Siddur Yaavetz; Kitzur SH”A 3/4; Aruch Hashulchan 2/7; Likkutei Mahrich “Levishas Habegadim”; Miasef Lechol Hamachanos 2/15; Beir Moshe 2/3
 The Reason: Although when placing on or removing clothing honor is given to the right side, as explained above, nevertheless by tying laces, honor and precedence is given to the left, as the left arm was honored by the Torah to have the Tefillin wrapped on it. [ibid]
 Mishneh Halachos 13/3; Piskeiy Teshuvos 2/5 and other Poskim mentioned there in footnote 38
 Piskeiy Teshuvos ibid