In the first aliyah, the Torah gives the mitzvah of the first fruits. After the people are settled in Israel, a farmer takes the first of the fruits of his crop to the Temple in Jerusalem. He goes together with the other farmers in his area in a joyous festive procession accompanied with music and song, led by an ox with gilded horns.
Upon arrival in the holy city, may it be speedily rebuilt, the farmer gives the first fruits to the priest and says a prescribed statement about how the Jews, from Yakov avinu's time to the present, got to Israel with G-d's help. The farmer then rejoices for all the good that G-d has given him. This is done only with the seven fruits that Israel is praised for. The seven fruits are: Dates, figs, grapes, pomegranates, olives, wheat, and barley.
In the times of the Bais Hamikdash, Jewish landowners were required to separate from their produce three kinds of tithing: terumah, a gift for the Kohanim, maiser rishon, the first tithe which is given to the Levi, and maiser sheni, which the farmer himself would go to Jerusalem and eat. And in the third and sixth years of every seven-year Shmittah cycle, the farmer would replace maiser sheni with maiser anni, the tithe for the poor.
In this, the second aliyah, the Torah gives the procedure to be followed every three years when the farmer is to declare that he has performed all his tithing properly. At the end of the aliyah we find that when the farmer finishes his declaration that he has done all the tithing properly, he then asks G-d to look down from His Holy residence in heaven, and bless the people and the land.
In the third aliyah Moshe admonishes the Jewish people to observe all of G-d's commandments and walk in His ways because G-d has set us apart as a treasured people. This aliyah begins with the words: Hayom hazeh -- This day your G-d commanded you... Rashi says this means that every day we should view the commandments as though we were commanded that very day. And the words V'shamarto v'osiso osom -- you shall therefore observe and do them... Rashi says that this alludes to a divine voice that blesses the farmer: "you have brought first-fruits today, you will be found worthy to bring them again next year."
In the fourth aliyah Moshe and the elders of Israel command the Jews that when the Jews pass over the Jordan they should set up twelve great stones and write the Torah on them in seventy languages. There is a commentary that says these stones served as a sort of mezuzah for the land of Israel.
In the fifth aliyah the Jewish people are told that on the day they enter the land of Israel, six of the tribes should stand on mount Gerizim and six on mount Eival. The elders of the Leviim and the Aron Hakodesh (holy ark) would remain in the valley between the mountains. The elders would alternately face each mountain, and, according to the Midrash, alternately state a blessing, then a curse until twelve blessings and twelve curses were stated.
After each blessing and after each curse all the Jewish people were to answer "amen". At the end of the aliyah G-d promises freedom from material worries and blessings of abundance for hearkening to His word.
The sixth aliyah contains G-d's warning of terrible punishments and prophecies of exiles for the Jews if they don't heed the Torah and serve Him with joy. It is a custom in many communities, that the Torah reader says the brochos for this aliyah without being called to the Torah by name by the gabbai.
In the seventh aliyah Moshe states that the Jews saw what G-d did for them in Egypt and in the desert for the last 40 years. Moshe continues: that therefore, they [and we] should observe and do the words of this covenant that G-d has made with us, so that we may prosper.