A number of studies show that having caffeine 30 to 90 minutes before a workout does indeed benefit you in several ways.
It decreases perceived effort (makes exercise feel easier), makes you more resistant to fatigue, and especially with high-intensity stuff like sprinting and cycling, increases power output and the number of reps you can perform before failing, and last but not least, boosts strength and muscle endurance.
In short, caffeine makes for better workouts in just about every way, but you have to take enough. Some studies have shown performance benefits with dosages as low as 3 mg per kg of body weight, but 5 to 6 mg per kg is more common and generally accepted as the “optimal” dose for maximizing benefits while also mitigating unwanted side effects.
To put those numbers in perspective, 6 mg per kg would be about 300 mg for a 120-pound woman (~3 cups of coffee) and 500 mg (~5 cups) for a 180-pound man. That’s much more than most people ingest before training, which is usually closer to 100 to 200 mg.
If you’re new to caffeine, I’d recommend starting at the lower dosage of 3 mg/kg to assess tolerance and move up to higher dosages if you don’t experience any serious side effects.
You should also know that research shows that the higher your caffeine tolerance, the less it will enhance your performance (and your body begins to develop a tolerance almost immediately). Therefore, if you want to get the most training benefit from caffeine, I’d recommend that you use it just a few days per week before your most difficult workouts.