Introduction

First, let us recall what's going on here. SR is about how different inertial observers are related, that is, observers moving at constant speed with respect to each other. We will always take one frame to be 'at rest' and the other frames to be 'moving' in our calculations. This is extremely important because the answers to questions like 'where or when did $x$ happen' depend on the state of motion of the observer.

Remember, even though we're looking at multiple reference frames drawn on the sheet of paper, we have to imagine ourselves being only one of them at any one time - usually the one at rest with respect to us (ie, our own reference frame). The most complications arise in SR when we try to imagine ourselves in two different frames at once and hitting contradictions. As long as we remember we can only be in one frame at a time, we'll do fine (nothing can be moving and not moving at the same time. If we attempt to imagine ourselves in this absurdity, no wonder we find other absurdities waiting for us).