In general, the Internet in Iran is not very fast, But it will meet your needs for this trip.
During your stay in a hotel you can easily access its Wi-Fi connection. Just ask for the Wi-Fi passcode when you check-in.
Also, if you buy an Iranian SIM card, you can easily connect to a 3G network. Read more about the SIM card.
It should be noted that many sites, such as Facebook and Twitter, are banned in Iran, and you will not be able to access them. However, this will not be a big problem; you use a virtual private network (VPN). Using VPNs in Iran is common,and many people use them to access websites which are not controversial in many countries, but banned in others. So don’t be surprised if an Iranian would like to contact you via Facebook.