Since this parsha has the "famous" VaYehi Binso'a Aron, I decided to talk about standing for a sefer torah.
The gemara says that since we are obligated to stand for a talmid chacham, kal v'chomer one must stand fro the sefer torah itself. However, the Taz writes in Yora Deia 242:13 that if the sefer torah is in its own mokom, defined as an area surrounded by mechitzos 10 tefachim high and 4 tefachim wide, then you do not have to stand. The Mishna Berura brings this down l'halacha in the Sha'ar Hatzion (146:18) as well. However, even though there is no chiyuv, the minhag is to stand for kovod hatorah.
The question is what about when the sefer torah is on the shulchan? Well, if the shulchan is on a real bima that is surrounded by mechtizos so then it is in its own reshus and there is no chiyuv to stand. Even if the shulchan is a standalone shulchan but it has sides then it is also not a problem. The problem really comes up when the shulchan is a regualr table with 4 legs. Since there are no mechitzos, it can not be considered a separate reshus.
There is a machlokes between the Pri Megadim and Rav Moshe what the halacha is.
The Shulchan Aruch in Y.D. Siman 242:18, the Mechabeir paskens that if your Rebbi gets an aliyah you don't have to stand up for him when he is standing by the shulchan. The Rema adds that you also don't need to stand if the bima is a separate reshus. The question is how does one understand the Rema. Is he saying a totally different din than the Mechabeir or is he explaining the Mechabeir? The Pri Megadim (Mishbitzos Zahav end of Siman 142) writes that the Mechabeir and Rema are saying two different halchos. The Mechaber is telling you that you don't have to stand because your Rebbi is in his place. The only time you have to stand for your Rebbi is when he is in transit,or temporarily standing to rest. Since in our case he is not in transit you don't have to stand.for him. The Rema is telling us a different halacha of reshus acheres-being in another reshus. The Pri Megadim concludes that since the halachos of standing for a Rebbi and a Sefer Torah are the same, when the Torah is also not in transit one does not have to stand. Therefore, even if the Torah is on a regular table you don't have to stand. Rabbi Akiva Eiger (Y.D. 242) and the Mishna Berura (146:17) both seem to agree with the Pri Megadim.
Rav Moshe (O.C. chelek 1 Siman 175) disagrees. He argues that the Rema is just explaining the Mechabeir and both of them are talking about the halacha of reshus acheres. His rayah is the fact that by standing for a Nasi, the Rambam writes you have to stand until he is seated. By a Sefer Torah the Rambam says you only need to stand while it is transt, implying when it reaches its place even if it is still standing you don't need to stand. (The Pri Megadim learns the Rambam by Nasi as lav davka-you don't need the Nasi to davka be sitting). Rav Moshe explains that really you can only sit when the Sefer Torah is seated. However, there is a fundemental difference between a person and a Sefer Torah. A Torah doesn't stand or sit. It is always being held. When the person carrying the Torah is no longer oin transit, the Torah is now sitting-sitting in the person's arms since a person is also a reshus acheres.
However, when the Torah is on a table, it is not considered sitting. But you still don't need to stand. The reason is because once the Sefer Torah is in its mokom there is no chiyuv to stand. The mokom for the Torah at this point is on the shulchan. so you can read from it. Therefore, you can sit down.