How to take off shoes by Halacha? Is there different minhagim? Shoes I mean with shoes laces and without buckles etc
There are different opinions to this. The Shulchan Aruch O:CH 2-4,5 says that regarding putting on shoes, that the right one is put on, and then the left, but the left is tied first and then the right. However, in the next halacha regarding taking them off the Shulchan Aruch just says simply, take off the left before the right, and he doesn’t say to untie the right before the left. Additionally, most poskim don’t comment on this, that the right should be untied first. Therefore, some poskim say that we just simply untie and take off the left shoe, and then untie and take off the right one. Others however say that since the left has the prominence regarding tying, it also has the prominence regarding untying, therefore the right should be untied first, then the left, then take off the left then the right. Bottom line, I can’t tell you what to do, however Piskei Teshuvos says to untie and take off the left and then the right.
(Note- for left handed people, who anyways tie the tefillin on their right hand, the right has the prominence regarding putting on and tying, (see M:B 2-6) therefore the question is not applicable, and the when taking off the shoes the everything of the left would come before the right.)
Bais Baruch (Miluim to Siman 1 note 39), Oz Nidberu 5-26 (3), Shulchan Melachim 3-13, Be’er Moshe 2-3 in the name of Maharalach, Piskei Teshuvos Siman 2-7.
As a side point, in your question you mentioned that you are asking about laces and not buckles. The poskim discuss whether these halachos apply to buckles, buttons, Velcro, zippers, etc. The Levush says that there are two reasons why we give the prominence to the left regarding tying shoes, because the tefillin is tying on the left hand therefore left is the prominent one regarding tying, and because of the pasuk “מחוט ועד שרוך נעל”, therefore the tying of the shoes is similar to the tying of the tefillin. The difference between the two reasons would be closing buttons etc. and closing other articles of clothing ( sleeve buttons etc.). If the point is that regarding tying the left is more prominent, then any type of closure would be the same as tying. However according to the second reason, it is limited to shoelaces. See Leket Hakemach Hachadash 2-19. Also see Rivivos Eprayim 1-5 that according to Siddur Ya’avetz, Shulchan Aruch Horav, Likutei Maharich, Aruch Shulchan, Kitzur Shulchan Aruch and Be’er Moshe (ibid) that this applies to all tying and not only shoelaces.
Another point, regarding women the opinion of R’ S. Z. Auerbach zt”l (Halichos Shlomo 2-20) is that they can just untie the left shoe and remove it, since women don’t have the mitzva of tefillin, this halacha doesn’t apply to them. However, Rivivos Eprayim (ibid) Be’er Moshe (ibid), and Shevet Hakehosi 1-6, say that since it is a prominence of the left over the right for tying, it would also apply to women.