Honestly there is a world of difference between the Weber Smokey Mountain Smoker and other models that look very similar. Those fall under the generic name of ECB or El Cheapo Brinkman, but similar smokers manufactured by different manufacturer's are in the same generic category.
If you have the Weber, great. More likely you have an ECB.
You can make decent Q with an ECB, but you are going to have to work at it and do some research. It takes some effort to keep a good low and slow fire going for 6 to 8 hours with one of these. Google "ECB mods" to learn how to modify your smoker to make it more suitable for true smoking. Start with a pork butt of around 6-8 pounds. Keep cooking these until you get it right, then you can branch out to other meats.