As far as I'm concerned, a RDM shouldn't be engaging in combat at even lower levels. While that may be what SE had intended when they created RDM, in a party situation, a RDM is rarely geared towards melee battling. Of course there's always circumstances where it may be permissable, but it's safe to adopt the policy of not allowing your party's RDM to melee in an exp. party.

As others have mentioned, RDM excels in enfeebling spells, moreso than any other job. Enfeebling the mob right off the bat has always been my priority at the beginning of any battle. That should be your RDM's first concern. Later there's dispel, which is used as needed and pretty self explanitory. At level 41 RDM become responsible for refreshing the other casters. This can become quite a pain, and it only gets more annoying at level 48 when RDM learns haste.

A RDM's role in the party is entirely dependent on what other mage classes are present in the party. More often than not, I end up being the main healer in place of a WHM, or perhaps I split the responsibilites of healing with a SMN or another RDM. On some rare occasions I've substituted for a BLM, but those are, as I said, rare occasions.

As Miriel pointed out, RDM are consider the Jack of All Trades (take a look at my new custom title; it's there for a reason) because of this flexibility. I find that RDM works at its full potential with both a BLM and a WHM present in the party, more specifically post-refresh. This allows a RDM to focus on enfeebling and maintaining the refresh/haste cycle while throwing in necessary bursts and heals. What people need to be most wary of is stretching their RDM to thin. There are many who seek to abuse RDM by making them do all of these jobs at once.

That's it in a nutshell without going into the pros and cons of the various subjobs that RDM can use. There's a lot more once you get into that.