When one is called to the Torah, he should go immediately and not delay (Mishneh Berurah 141:25). The reason is because one should display kavod hatzibbur (being courteous to the congregation) and also kavod hatorah (honoring the Torah) by demonstrating how dear the Torah is to him (Mishneh Berurah 141:22). Similarly, one should take the most direct way on his way to the bimah and the longer way back after his aliyah, to show that leaving the Torah is difficult for him (Aruch Hashulchan 141:9).
The oleh recites Barchu before reciting Birchas Hatorah (Shulchan Aruch 139:6). The tzibbur responds Baruch Hashem Hami'voruch L'olam Va'ed, in order to show that they also want to be included in blessing Hashem (Shulchan Aruch 139:7). Afterward, the oleh recites Birchas Hatorah; the brachah of Asher Bachar Banu before krias hatorah and Asher Nassan La'nu etc. afterward.
Before one recites the brachos, he should open the Torah and look at the place where his aliyah starts (Shulchan Aruch 139:4). When reciting Barchu and the brachos before reading, he should keep the Sefer Torah open, because it is considered tircha d'tzibbura (inconveniencing the congregation) to close and then reopen the Torah (Mishneh Berurah 139:17). As an aside, Rabbi Yissochar Frand, shlit"a, points out that we see how important the honor of the tzibbur is. Even though opening and closing will only add merely a few seconds; Chazal were still careful that one should not inconvenience other people (Parshas Balak-5768)!
The Rama [139:4] suggests one to turn his head to the side [so as not to seem as if he is reciting the brachos written in the Torah]. However, the Mishneh Berurah [139:19] brings an opinion that it is not proper to physically turn one's head away, rather one should close his eyes. One should recite Barchu and Birchas Hatorah in a loud and audible voice in order that the tzibbur can answer amen (Shulchan Aruch & Rama 139:6). The Mishneh Berurah [139:24] explains that as long as 10 people heard him recite Barchu it is sufficient.
While one is reciting Birchas Hatorah one should hold onto the handles of the Sefer Torah (Shulchan Aruch 139:11). The Mishneh Berurah [139:35] adds that one should also hold on to the Torah the entire time it is being read.
There is a minhag to slightly lift up the Sefer Torah while reciting the words V'nassan La'nu Es Toraso (and He gave us His Torah) and V'nassan La'nu Toras Emes (and He gave us the truthful Torah) to show that this is the Torah that Hashem gave us (Aruch Hashulchan 139:14).
The oleh should recite the leining quietly along with the baal koreh during his aliyah, in order that his brachah is not a brachah le'vatalah (Shulchan Aruch 141:2). Both the oleh and the baal koreh should stand (Shulchan Aruch 141:1). Someone who has difficulty standing may lean on something a little bit (Shulchan Aruch 141:1 & Mishneh Berurah 141:4). The oleh should wear a tallis (Mishneh Berurah 14:11 & Aruch Hashulchan 91:2).