For an even more reliable playback “at speed,” switch to the bounding box view. It’s very abstract but can give you a better idea of the actual playback pace if using wireframe mode is still too slow.
In terms of adjusting a particular object’s animation speed, the simplest way is as mentioned, just grab some keys in the DopeSheet or Action Editor and drag them so the start & end of your action brackets fewer frames. But you can do this with more efficiency & accuracy as well by scaling a set of selected keys. The frame indicator acts as the “pivot” point for such scaling.
For example, say you have a ball-bounce that takes 5 seconds and want it shortened to 4 sec. In the DopeSheet or Action Editor (or even the F-curve Editor), grab all the keys in that sequence, place the frame indicator at an appropriate place on the Timeline (often on the first frame of the sequence), then use S-KEY (for Scale) and type 0.80 for the scaling value. The selected key sequence will then shorten to 4 seconds (5 x 0.8 = 4) with all the keys in the sequence being adjusted proportionally. Making a sequence longer just means scaling by > 1.0
In the F-curve Editor you can make things go “faster” but keep the same sequence length. This is done by adjusting the slope of the animation curve(s) for an object. The steeper the slope (which is a relative thing given that you can adjust the view so freely), the faster the object will perform the transform you’re adjusting.
For example, a fan’s rotation over a given set of frames (say 24) can be sped up by increasing the slope of the f-curve for the rotation axis on which the fan spins. If the first frame is at 1 and the last at 24, grab the key at frame 24 and drag it in Y (“up” for a positive slope and “down” for a negative slope) in the F-curve Editor. You’ve increased the amount of rotation per frame (that’s what the Y-axis is for, it denotes the value of the key you’re moving) and thus the fan spins faster.
Note about slope adjustment – slopes can be positive or negative, so the direction in Y that you drag a key is dependent on which way the slope runs to begin with. If it’s a negative slope (Y values decrease with time so the slope is going “downhill”), you’ll want to drag the Key in negative Y – “down.” For positive slopes (“uphill”), drag the keys “up” in positive Y.