A dedicated line connection can service multiple networked computers. It is a 24 hour high speed connection.
Dialup connections allow a single computer to access the internet over a phone line.
This option is easy to acquire and use and is relatively inexpensive. The speed of this type of connection is dependant upon the ISP and your modem. The benefit of a commercial online service is that they provide you with all the software that you need. The disadvantage is that their access tends to be slower and often limits you to using only their software. Also, you are generally billed based upon time connected - which can be expensive.