Welcome, gentle reader.
It is assumed you know what an IP address, a network address, a netmask, routing and DNS are. If not, I recommend that you read the Network Concepts HOWTO.
This HOWTO flips between a gentle introduction (which will leave you feeling warm and fuzzy now, but unprotected in the Real World) and raw full-disclosure (which would leave all but the hardiest souls confused, paranoid and seeking heavy weaponry).
Your network is not secure. The problem of allowing rapid, convenient communication while restricting its use to good, and not evil intents is congruent to other intractable problems such as allowing free speech while disallowing a call of ``Fire!'' in a crowded theater. It will not be solved in the space of this HOWTO.
So only you can decide where the compromise will be. I will try to instruct you in the use of some of the tools available and some vulnerabilities to be aware of, in the hope that you will use them for good, and not evil purposes. Another equivalent problem.
(C) 2000 Paul `Rusty' Russell. Licenced under the GNU GPL.