I have a pretty standard 4 port ASDL router. I am running out of ports so wondering if I can piggback the spare 4 port router I have or if I need to purchase a new 8/16 port router. If it can be done, how is it done (I am sure it is simple, but so am I).
it's enough if you buy ethernet switch and connect it to one of lan ports of your router.
but yes - you can as well daisy-chain router behind router and have two layers of nat. but then communication between computers linked to first level router and those behind 2nd router will be a bit tricky.
As pQd said, probably the best solution is to buy a 8/16 port Ethernet switch and expand your existing network. If your needs grow again, you can take another port and connect another switch allowing you to expand further.
Just be careful if you connect switch-to-switch that you don't cause a STP loop. See this post for some more details:
The risk you will run by connecting one router to another is getting the routing setup properly. Most home 'routers' also act as firewalls which means you will be unable to communicate between the two networks without some additional configuration. You will also need to either run a routing protocol (RIP or OSPF probaby), or setup static routes so everything communicates properly.