I am a student and I have to go to Italy for a conference in mid-May for a week. Then I have to go to Germany for another conference in late September for a week. A Schengen visa is valid for 90 days only, so how will I manage going to Germany if I use my visa in May for Italy?
A Schengen visa isn't necessarily or usually valid for 90 days. It's often limited to a specific number of days of stay over a given period.
If the visa is also a multiple-entry visa, you can use those days as you see fit, e.g. staying a few days in Italy for your conference, going back to your country of residence (or, at least, out of the Schengen area) for some time and then coming back to the Schengen area for the conference in Germany.
But if the visa says “90 days” in the “duration of stay” field, it actually means “90 days over any 180-day period”. Consequently, it would be perfectly fine to stay for a couple of months in May-June, leave and come back in September for some time. If there are at least 90 days between both stays, you could even stay three months each time (say mid-April to mid-June and mid-September to mid-November).
Of course, that's only possible if the visa is valid over the whole period. If you apply for a visa for the Italy conference and its validity does not extend to September, you will need to apply for another visa. But do not use all your 90 days during the summer, as the maximum stay rule applies across visas. If you stayed in the Schengen area in May-June-July, you would not be able to re-enter in September.
The only thing you cannot do is stay without interruption between May and September. To do that you would need another purpose (two brief conferences do not justify a 5-month stay) and another type of visa.