Why is it called Shabbat HaGadol?
- Some explain that it's called Shabbat HaGadol because that was the Shabbat when a miracle occurred for the Jews in Egypt that the Egyptians didn't say anything when the Jews took sheep, which was the Egyptian god, in order to slaughter them for Pesach.
- As Am Yisrael left Mitzrayim on the 15th of Nissan (Thursday), the previous Shabbat would have been the 10th of Nissan, the same day Moshe asks K'lal Yisrael that "they shall take every man a lamb, according to the house of their fathers, a lamb for a house."  Tosfot  explains that this action interested and angered the Egyptians, and so the firstborn pleaded to Pharaoh to free Am Yisrael, but he refused. And so, as a result, the firstborn attacked their fathers. The greatness is derived from the damage Hashem did to Egyptian society in this sense.
- See Sfat Emet Shabbat HaGadol for more.
- It wasn't established on the date of the 10th because it was the date of Miriam's death and we don't want to establish a holiday for that day.
- There are a number of Minhagim about which Haftara to read when Erev Pesach is on Shabbat HaGadol, and each community should follow its own custom.
Drasha of the Rabbi
- The minhag is for the Rabbi of the community to give a Drasha on Shabbat HaGadol on Hilchot Pesach. If Shabbat HaGadol falls out on Erev Pesach, the Drasha should take place a week earlier.
- If the Rabbi who usually gives the Drasha on Shabbat HaGadol is in mourning and there’s no other Rabbi to make a Drasha, it’s permissible to give the Drasha. 
Greetings on Shabbat Hagadol
Reading the Haggadah in advance
- On Shabbat HaGadol, the minhag is to read the Haggadah from Avadim Hayinu until LeChaper Al Avonotanu. 
- Shulchan Aruch O.C. 430:1, Mishna Brurah 430:1
- Shabbat 87b
- Aish.com citing Shemot 12:3
- Aish.com citing Midrash Tehilim 136:6 and Ancient Tanchuma Bo 18
- Magen Avraham 430:1
- Yechave Daat 1:3
- Mishna Brurah 429:2, Chazon Ovadia page 32
- Mishna Brurah 430:2, Chazon Ovadia page 32
- Halichot Shlomo (vol 1, 2:7)
- Chazon Ovadia page 29
- Rama 430:1 based on Ravyah 225 writes that the minhag is to read the Haggadah from Avadim Hayinu until LeChaper Al Avonotanu on Shabbat HaGadol. This is quoted by Kitzur Shulchan Aruch 107:3. However, Beiur Halacha s.v. BeMincha quotes the Gra (Maaseh Rav #173) who didn't have the minhag to read the Hagadah on Shabbat.