There are a couple of books out there that can help you in that process.
I would suggest the most common way is to refer to a copy of the Mallory Yaxely Encyclopedia and its various editions. Mallory lists each brand by their model numbers, number of tubes and type in each model and whether that model is in Rider. Not all models are listed and those that are are not often in Rider particularly the earlier ones. If the tube lineup is a common one for the brand you can often consult Rider for the physical layout of the chassis in the service lit to confirm the model. An example of that is on Ebay now:
http://tinyurl.com/4gcgot
If you don't know the manufacturer and have a not so common tube line up you can often filter out what you have by scanning the line up of all the models in Mallory. An easier way would be if you had a copy of
The Locator by Gerald Larsen. Larsen listed by the number of tubes in each set and where they could be found in Rider Volumes 1-23. Here's a review of that book by AR Classified. I don't think its widely circulated but as of last year copies were still available I believe from his widow at that address at the bottom of that article.
That link:
http://www.antiqueradio.com/bookrev2_06-98.html
An online version of that of sorts can be accessed at :
http://www.grillecloth.com/sylvania/tubelist.php
Finally it's often helpful to know who made what in cross referencing brands to manufacturers. Although it doesn't cover everything the Radio Trade Name Directory located here can often help you point in the right direction. (Some consult Radio Museum dot org as well)
That link:
http://www.radioremembered.org/
Hope that helps
Best Regards
Ken Walsh
Cape Breton Island