I have 3 cisco 2821 routers for home lab studying for CCNA. When I bought them I didn't think about the connection issues that I might face. They have only 2 gigabit ports and for many of the labs it looks like I need more. I'm trying not to buy anymore equipment i.e HWIC cards. I've looked up connecting routers by the AUX ports but cannot find a specific document. I saw one showing how to connect back to back but it still needs a serial interface which I don't have. Any way to connect just using the AUX ports and what cable do I need? Thank you.
The AUX port is a serial interface used for managing the router itself. It cannot be used as a network interface, i.e. for sending/receiving routed packets.
If three routers are enough for your lab, and you just need lots of interfaces, you can try connecting them up like this (since you say each router has two interfaces available):
+-------+ +---------+ | | | R2 | | | | +-------+ | +---+---+ | +----+ | | R1 | | | +----+ | +-------+ | +---+---+ | | | +---------+ R3 | | | +-------+
and then create as many sub-interfaces on each physical interface as you like. These sub-interfaces will show up in the running-configuration as independent interfaces allowing you to, for example, create a network with hundreds of interfaces, subnets and so forth.
Here is how you connect the AUX ports of old school Cisco routers (e.g. c4700, c7200) together using a null modem cable and PPP. It worked last time I tried it (back when IOS 11 was the hot thing). I have never tried this on a newer router like your 2800s, but I assume it's still possible assuming you build the right cable. YMMV.
That said, while it's a cute hack, your Cisco education will probably be well served by listening to @mere3ortal and learning all you can about sub-interfaces. You'll use sub-interfaces a lot.