He joined the biggest manga publishing company,Shueisha,and started a short comic for the Shonen Weekly Jump, magazine/newspaper. His first published manga, Wonder Island, was pressed in December 1978. It wasn't sucessful, but his second Manga Dr. Slump was. This got him started. After eight years of this moderately successful series, he ended Dr.Slump.
After this he created Dragonball. Dragonball didn't really become succesful until the Tenkaichi Budouki. From then it just popped up and became very succesful. The next thing to do was make a television series.After it ended, people kept wanting more. So next came one of the best things in history...Dragonball Z. DBZ appealed to a wider audience. In Japan they have 5 different types of Manga and Anime. There is the young boys, the young girls, teenage boys, teenage girls, and adult anime (no I'm not talking Hentai). Well dragonball z fit into all these catagories, while his other series pretty much fit into the young boys and girls, and maybe teenage boys. Dbz became a show and the rest is history.
Dbz was ended in 1995 partly because Akira Toriyama was tired of working the long hours, often until 4 in the morning. He had little time for his family. It usually took him 5 days to make up and draw a comic. Toriyama liked to take his time making mangas, and the busy schedule was to much for anybody.
After DBZ Toriyama worked as a consultent for Dragonball GT, a creation not from him. GT was more created for the younger audience than DBZ. Also after DBZ he worked as a Character designer for many games including Chrono Trigger, Tobol #1, and Dragon Warrior. He also did several short stories, such as "Alien X" and "Cowa" And from what I hear is working on another series called "Kajika".