Should I use a Column naming convention or rely on column descriptions? Frankly I am stunned that after some basic (very basic) internet searches I have not been able to find a comprehensive naming convention or guideline or SQL object and column naming.  

The parallel I'm used to is in the .NET development world where there are many offered conventions and Microsoft has gone so far as to document a comprehensive set of recommendations which is widely adopted:


General Naming Conventions 
Design Guidelines for Class Library Development 
Guidelines for Names


1. Is there a well-adopted standard for database object, column, etc naming?

2. Are there any pitfalls with relying on the Description property for describing columns of a table? Obviously one wants the name to reveal intent but that's sometimes difficult in a database and descriptions can be invaluable for someone learning about the DB (although they can also lie).

Help much appreciated!
Pick a standard, make sure it makes sense, and document it. There have been plenty of debates about this (e.g. whether the identity column in the contacts table should be called ID or ContactID, or whether the contacts table should be called dbo.Contacts or the unnecessarily verbose dbo.tblContacts), and you're never going to find agreement among your peers. Which standard you choose is not important; what is important is that you use it consistently, make it well-known, and get agreement from your colleagues that this is the way.
Your columns should be self-documenting (and not cryptic, abbreviated or obfuscated) where practical. I would NOT rely on the extended properties, but that's just me (google/bing for problems with extended properties and you will see plenty of complaints I would guess). External documentation / data dictionary is much more valuable to me - if your database goes south and so does your backup, it makes it that much easier to rebuild. It also makes it easier to describe your schema to junior developers etc. without giving them direct access to everything.