I have been using Crossover for years, and I have never had the problem your describe. Would you mind telling the class what distro you're using? It would also be useful to know what desktop environment you use, so as to figure out why you don't have a menu entry anywhere to allow you to start Crossover after installation.
Anyway, you should have two directories, the .cxoffice is for your "bottles" or "prefix" and usually in your home. There should also be a cxoffice, without the dot, somewhere on your system. If you used a deb or rpm, it will probably be in "/opt/cxoffice". If you have used the bin file, you could have Crossover in a "single user" installation, in which case cxoffice would also be in your home. All of this is in the manual, which clearly, you didn't read.
As for the origin of the problem, I suspect you're missing some librairy which is necessary for a smooth operation. In the cxoffice/bin folder, you could run cxdiag in the terminal which would help to diagnose the problem. A bunch of the libraries listed won't be crucial, but there might be one that is.
Lastly, even if you have the trial, I believe you can enter the equivalent of a support ticket by writing to info@codeweavers.com. I'm sure the staff will sort your problem out in no time. It will surely be more to the point than the forum.