As mentioned last week, there is a Rabbinic obligation to read the weekly parshah. There are numerous ways that one may fulfill this mitzvah in a preferablefashion. The earliest time one may start learning the parshah, is at Mincha time of the preceding Shabbos (Mishneh Berurah 285:7). For example, starting at Mincha time of this Shabbos [Parshas Vayeira], one may start learning next week's portion [Parshas Chayai Sara]. The reason is, since the congregation starts reading the following week's parshah by Shabbos Mincha, it is considered as reading the parshah together with the congregation (Mishneh Berurah 285:7). Regarding shenayim mikra, "Mincha" is referring to Mincha Gedolah [which is the earliest time one can daven Mincha (usually around 1 PM)], since this is the earliest time one can begin the following week's leining (Shemiras Shabbos Kehilchasa 42:ftnt. 218).
There are numerous opinions when is the ideal time to finish the parshah. Some Poskim are of the opinion that it is preferable for one to finish on Friday, while others hold before going to shul on Shabbos morning. Still others hold before leining in shul or by the time one starts his Shabbos morningmeal. Some say it should be done by Shabbos Mincha (See Shulchan Aruch 285:4 & Mishneh Berurah 285:7-9). If one did not finish on Shabbos, it is preferable to finish by the following Tuesday (Mishneh Berurah 285:11). The reason is the Gemara [Gittin 77a] teaches that Sunday, Monday, and Tuesday are still connected to the previous week.
Ideally, one should make sure not to read targum first, before any mikra (Mishneh Berurah 285:6). If he did, he does not need to repeat what he learned (Shaar Hatziyon 285:10 & Aruch Hashulchan 285:3).
Most opinions hold that one has to actually read himself shenaiyim mikra v'echad targum, and it does not suffice to hear it from someone else (Mishneh Berurah 285:2 & Aruch Hashulchan 285:3). Additionally, if you know how to lein with the trup, it is proper to learn shenaiyim mikra with the trup (Sefer Bekeurei Chaim 3:4 quoting Rabbeinu Yonah Sefer Ha'yirah 303). One may quietly read the leining along with the baal koreh to count as one time mikra (Mishneh Berurah 285:14 & Aruch Hashulchan 285:3). It is important to note, that one is also required to hear the leining, so one should be careful to hear the baal koreh while reading (Mishneh Berurah 285:14). Someone who is practicing leining, counts towards the obligation (Sefer Bekurei Chaim 7:25).
One should be careful to read the parshah in order, and not skip around (Mishneh Berurah 285:6). If one did accidentally skip, he may read the posuk that he missed [and is not required to go back to that point and continue straight] (Sefer Bekurei Chaim 3:2).
There is a machlokes whether one may interrupt [with talking] while he is in the middle of learning shenaiyim mikra [and not at a "stopping point," e.g. in between parshiyos]. The Chofetz Chaim [Shaar Hatziyon 285:11] holds it is prohibited, however the Aruch Hashulchan [285:7] holds there is no problem
If one is in question whether he already learned shenaiyim mikra [e.g., he does not remember where he got up to], it is proper to go back to the place he for sure read (Chut Shani, Shabbos 4: pg. 113 s.v. me & Koveitz Halachos, Shabbos 1:19:37).