Personally, I prefer to visit the website. Some manufacturers have a gluten free product list in their FAQ or customer service section. If not, you can send an email asking if they have a gluten free product list, or if they don't, what their gluten labeling policy is. Some manufacturers only disclose wheat, while others go the extra mile and disclose any gluten-containing ingredient in any amount.
Another important thing to ask about is whether the product is made on gluten free equipment and/or in a gluten free facility. If you tend to be more sensitive than most, like me, this information can be very helpful. When a product I'm really interested in falls into this category, I ask the company if they can give me more information.
For example, when a product is made in a facility that also produces products containing gluten, all it ends up being is that there's gluten-containing soy sauce in a product three lines over in the same building. Which is no problem whatsoever. It's not like soy sauce is going to splash 50 feet from that line into my barbeque sauce.
On the other hand, if products containing wheat flour are made in the same building, I'd be very leery about trying it. With the large amounts of flour and large pieces of equipment that food manufacturers deal with, the flour usually gets dumped into the equipment. That creates a puff of flour that goes up into the air. They actually say that flour can be airborne for many hours and it will drift and settle on everything.
As far as products that are produced on the same equipment as gluten-containing foods, I've been surprised at the effort that some manufacturers go to to keep gluten out of food that is produced on the same equipment. Some manufacturers completely disassemble and steam clean the whole line before making gluten free foods. Others clean the line as best as they can and then throw away the first run of gluten free food so they can make sure that any gluten that might still be on the line comes off the equipment.
If you're unsure of a product, the manufacturer's response doesn't reassure you, you can't find any alternative product, and you REALLY want to try it, what I suggest you do first is to run a EZ Gluten Test on it.
You could just try it and see what happens, but I'd be very careful about that. Especially if you're new to the gluten free diet. Until you're really good at recognizing your symptoms, you can end up glutening yourself for weeks without realizing that that product is why you're not sleeping well or you're yelling at your kids about everything. I don't risk it very often because I'd rather miss out on a food than have my symptoms. In the four years I've been gluten free, I think I've done this two or three times. Once I did it while we were tent camping and it was really bad. One of the worst glutenings I've ever had.
Another thing you can do is do a web search and see if you can find anyone who is gluten free mention the product and their experience with it, or an alternative product they have found to replace it. Gluten free people tend to be an inventive bunch.
Once you find a gluten free product list or find out a manufacturers labeling policy, check back with them every once in a while. Products are taken off gluten free lists and other products are added from time to time.
Check with your local grocery stores as well. Safeway actually has a full list of all of their store brand products that are gluten free. All you have to do is email them and they'll send you the current list.
So don't be afraid to verify new things and branch out. The more products you are able to verify, the more food options you will have.