If your gym is anything like mine, you probably have a wide variety of fitness equipment at your disposal. And if you're not familiar with strength training, this can turn the gym into an extremely intimidating environment. Some gyms will set up a circuit by numbering different pieces of equipment. This helps the beginner know where to, well...begin. But if there aren't any numbers in sight, or if you've chosen to strength train in the privacy of your own home, knowing where to begin is still a battle that you'll need to face. So without further ado, I give you my advice: quads first, calf muscles last.
In other words, always train your biggest muscles first. Quadriceps, hamstrings, gluteus maximus, core, chest and back muscles. The various exercises that work these muscles can be quite demanding, so it makes complete sense to hit 'em while your energy level is fresh. Small muscles, on the other hand, exhaust easily which means you won't have to put forth as much effort. These muscles include your shoulders, biceps, triceps and calves. And so, start with your quads and move through the list until you hit your calf muscles.
If you don't have time for a total body workout, it's perfectly acceptable to break things up. Just remember that whether you do upper/lower body or front/back workouts—the big/small rule still applies.