An Internet Lounge is a place set up with Internet access and computers for shared use by the convention members.
In the simplest case, the hotel may have one or two computers available in a Business Suite of some kind. The convention may be able to negotiate the use of these machines for the members at a reduced rate. This really would not be adequate for a convention of any large size, but it might work for small gatherings.
Most commonly, the convention is able to scrounge donations of spare computers, and these are networked together to some high speed internet access available in the convention hotel. If you are very fortunate, your convention is rich or you have some local benefactor willing to loan you modern, state-of-the-art machines, ready to use. More likely, you will get machines just barely functional. For most conventions this is not a huge problem, since people are probably just checking email once a day or so. If your members complain, you might mention this fact to them. However, don't just take junk donations. Keep in mind your intended use and politely decline useless junk, if necessary. And be sure to provide at least one MS Windows-like computer and one Apple Mac-like computer, to accomodate users with limited computer skills and flexibility.
In addition to wired access, be sure to provide wireless networking for the members. This allows them to bring their own computers and connect as they please. Which simultaneously makes more wired computers available to members without their own computers.
Another variation is to get Internet service, either wired or wireless, added into the hotel contract. Most large hotels already have some kind of high speed Internet service that they would sell to guests anyway. If the convention can afford to make a blanket access contract for the members, they will probably save money. That decision would be a balance between convention finanaces versus the cost of access versus the probability the member will want to use it. If your convention is likely to take over the majority of rooms in a hotel, it might be worth it to you and the hotel management to negotiate a good discount rate, or even provide it free.
As with any good computer installation, be sure to harden against malware and vandalism. Install virus checker programs, install firewalls, and be ready to wipe and rebuild machines. They probably didn't have anything of value on them before you got them, and you definitely do not want to put them back into a trusted environment after they've been out in the public for several days.
Don't let people eat or drink while sitting at the donated machines. Avoiding spills and cleanup is just courtesy to the next user, and certainly the lender would like a clean machine returned to them.