I am new to Jewish observance and am a bit confused about what to do at the Passover Seder. More accurately, I'm not sure which of the traditional observances apply or not, and why or why not. For example, I know there's a mitzvah to sacrifice a lamb for Passover, at least in the Torah, but I'm not sure if that's done nowadays. But eating matza certainly is done, as well as other observances. So could you please shed light on this for me?
I commend you on your interest in observance and for asking such important questions.
The main reason why some of the mitzvot of Pesach mentioned in the Torah are not observed nowadays is because we do not have the Templein Jerusalem, and in particular, the altar upon which were offered sacrifices.
Therefore, the lamb that was commanded in the Torah to be eaten on the first night of Pesach cannot be performed. Similarly, since the bitter herbs mentioned in the Torah are to be eaten only with the Pesach lamb, this mitzvah is also not applicable nowadays. It is nevertheless customary to have some roasted meat or poultry (usually a thigh) on the Seder plate as a remembrance of the Pascal lamb. Regarding the bitter herb, it is actually a rabbinic commandment to eat it during the Seder.
That being said, there are other mitzvot of Pesach from the Torah that do apply even today.
As you point out, one is the eating of matzot as in the verse, "On the fourteenth of the month in the evening you shall eat matzot" (Ex. 12). Even though it was a mitzvah to eat the matza with the Pascal lamb, the Talmud explains based on verses that the mitzvah of eating matza is independent of the lamb, and therefore operative even in the absence of the altar.
Another Torah mitzvah applicable today is relating the story of the redemption and departure of the Jews from the bondage of Egypt as in the verse, "You shall tell your child on that day saying, 'As this G-d did for me when I came forth out of Egypt." (Ex. 13). The Haggadah (literally "the telling") that we read on this night is essentially a rabbinic formula for fulfilling this mitzvah of relating the miracles of the redemption. It is to be recited even if one has no child, and even if one is alone.
In addition to the rabbinic mitzvah of eating the bitter herbs, the Sages ordained another mitzvah especially for this night, which is the four cups of wine that correspond to the four different references to redemption in the Torah. Beyond these rabbinic mitzvot there are other rabbinic customs and practices such as: eating and drinking while reclining, dipping the carpas vegetable in salt water, dividing one matza and putting it aside for the end of the meal, eating the afikomen, and reciting special praises to G-d called Hallel.