It is permissible to use internet for any legal and allowable purposes especially for spreading the message of Islam. In case, however, it entails evil or is considered to be against the law, one should not use it.
We have forwarded your question to the offices of some grand religious authorities and the answers which we have received are as under:
Grand Ayatollah Khamenei (may Allah grant them long life):
Generally speaking, if it (using internet) entails any evil (such as spreading corruption, false and incorrect dogmas), or it is feared that one might commit a sin or it causes the enemies of Islam and Muslims to be strengthened or it is against the rules and regulations of the Islamic Republic, it is not permissible.
Grand Ayatollah Makarem Shirazi (may Allah grant them long life):
If it is against the law and entails evil, it is not permissible.
Grand Ayatollah Saafi Gulpaigani (may Allah grant them long life):
Generally speaking, people who do not have sufficient and precise understanding of ideological issues, should use all available tools to repel doubts that have been cast and that they should get the society rid of misgivings because this is a manifestation of commanding good and forbidding from evil (amr bil-ma’ruf wa nahy anil munkar).
Ayatollah Mahdi Hadavi Tehrani (may Allah grant them long life):
It is permissible for a person to make legal use of internet especially when he intends to spread and promote the cause of Islam and the School of Ahlul-bayt (as). In case, however, using it (a certain website) is considered to be against the law, one must not use it.
Link to Isteftaat Website
 The question has been sent by the team of Islamquest website to the offices of some grand religious authorities including Ayatollah Khamenei, Ayatollah Makarem Shirazi and Ayatollah Saafi Gulpaigani (may Allah grant them long life).