It actually boils down to one of the "3B" techniques: bagging, boosting or blending.
In bagging, you train a lot of classifiers on different subsets of object and combine answers by average for regression and voting for classification (there are some other options for more complex situations, but I'll skip it). Vote proportion/variance can be interpreted as error approximation since the individual classifiers are usually considered independent. RF is in fact a bagging ensemble.
Boosting is a wider family of methods, however their main point is that you build next classifier on the residuals of the former, this way (in theory) gradually increasing accuracy by highlighting more and more subtle interactions. The predictions are thus usually combined by summing them up, something like calculating a value of a function in x by summing values of its Taylor series' elements for x.
Most popular versions are (Stochastic) Gradient Boosting (with nice mathematical foundation) and AdaBoost (well known, in fact a specific case of GB). From a holistic perspective, decision tree is a boosting of trivial pivot classifiers.
Blending is an idea of nesting classifiers, i.e. running one classifier on an information system made of predictions of other classifiers. As so, it is a very variable method and certainly not a defined algorithm; may require a lot of objects (in most cases the "blender" classifier must be trained on a set of objects which were not used to build the partial classifiers to avoid embarrassing overfit).
The predictions of partial classifiers are obviously combined by melding them into an information system which is predicted by the blender.