For lawyers: In general what are the mechanics for obtaining a writ of mandamus to compell a Court to rule?

Answers:
It depends what court and what the issue.
Normally, each level of court is under the supervising authority of a higher court. If there is a clear obligation to rule immediately, a higher court might issue a writ upon a proper request. What constitutes a proper request is governed by local court rules which normally put specific requirements on a petition for a writ.
You should be aware that writs of mandamus to compel a decision by a lower court are very rare. For the most part, a judge can take as long as needed to rule. It is almost impossible for a party representing themselves to get a writ from a higher court. Most attorneys, having to appear in front of that judge again on other cases, are reluctant to file for a writ -- knowing that it is unlikely to be successful and not wanting to tick the judge off in the absence of a good chance at success.
I would strongly urge you to talk with your attorney. Unless the case has been under advisement for a substantial period of time (e.g. more than six months) and the failure to get a ruling is adversely effecting you in ways beyond mere uncertainty, you are unlikely to succeed and your attorney will properly advise you against pursuing a writ (especially as the judge could rule against you in ways that would hurt you on appeal after the writ issued).

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Subtly slipping da judge a few samolians. (wink~rib~rib)