Basically, for almost anything, prune it just after it finishes flowering. (Partial exception being those very few woody plants that flower in fall, which should be pruned in late winter or early spring - think of it as 'as soon as they finish flowering, minus the "pause" of wintertime')
If the elder is too large for its space, you might seriously consider moving it elsewhere or getting rid of it, and putting something more space-appropriate there; you CAN continually prune elders back, even to the ground in many cases as long as you provide good growing conditions, but it is a lot of aggravation compared to growing something that is better suited to the space available.
As far as what "way" to prune them, essentially there are only 2 kinds of pruning cuts: removing a whole branch at the ground, which thins the plant out and opens it up (can also reduce its height mildly if you choose the tallest shoots to remove), and shortening a branch, which obviously 'smallens the plant down' but also causes it to grow bushier and with renewed vigor.
So you'd want to look at your mockorange and elder, and decide whether they need to be more open or more bushy. If the answer is "shorter but not more bushy", which is the most common situation for that kind of shrub, you would do both things -- take out the largest and/or most poorly-placed and/or most bare-at-bottom stems right at ground level, but also shorten some other branches back in a judicious way.
Remember that plants will normally start putting out branches from the one or several growth buds immediately below your pruning cut. (You can see these, if you look carefully, either on bare stem or in the axils of leaves). So you might want to locate any shortening-type cuts such that the growth buds that will take over are on the side of the branch where you WANT growth to go. For instance if you want the plant to grow more upwards not sideways, make any pruning cuts just above growth-buds that are facing upwards.
Good luck, have fun,
Pat