A question that involves velocity will have some sort of indication of a direction in which an object is moving. For speed, direction does not matter. Another way to say this is that speed is a scalar quantity; it involves only how fast an object is moving. Velocity is a vector quantity, and refers to how fast an object changes its position.
A way I used to teach this concept in physics is to have the students picture an athlete who runs once around a track, back to his or her starting point. The athlete's speed can be calculated by seeing how long it took to cover the 400 meters. If it took 200 seconds (a bit over three minutes), the athlete's speed was 400m/200s, or 2m/s. But because the athlete returned to the start, their velocity, or change in position per second, is zero.
When you look at your physics problems, check to see if there is a direction specified; if so, it is a velocity problem. If it is merely a "how fast" question, with no reference to direction traveled, it is a speed question. See the attached link for more information and some practice problems.