Magnets can be combined to either reduce or increase their strength, depending on their orientation to each other. Combining two equal magnets will not double their strength, but it will come close.
If the north side of one magnet is combined with the south side of the other, so that the poles are oriented N-S-N-S, then the strength will be close to double that of a single magnet, if they are the same shape and strength.
Less Than Double
The reason it won't precisely double is because the magnets don't occupy the same space. Although the field strengths are additive, the field strength on the top surface of the combined magnet is a distance away from the other magnet--namely, the width of the top magnet away--so the full effect of the bottom magnet isn't felt.
If the two magnets are combined so the same poles are facing, then their magnetic strength will be greatly reduced. They will not be completely canceled out, by the same argument as above: they don't occupy the same space.
A student might expect that combined magnets would cancel, like electric charges. But magnetic fields are instead additive.
Note that magnetism can be viewed, loosely, as created by the circles that electrons make in their orbits. If the orientation of these orbits is random, they'll cancel each other. If they're all oriented in the same direction, their effect is cumulative and the field strength is additive.