Let me expand Felipe's answer a bit.
Vélu's formulae given in the very readable short paper  are very easy to use. For instance if you are given a $n$-torsion point one can immediately write down the Weierstrass equation for the quotient by this point.
To get such a point, one can use the division polynomials which can be computed recursively very fast. The zeroes of this polynomial are exactly the $x$-coordinates of the $n$-torsion points. Oover the complex number it is not difficult to get them also using the parametrisation by the Weierstrass $\wp$-function.
There are quite a few paper improving Vélu's formula. Most importantly, there is Kohel's thesis . Or for instance . These were used in the implementation for isogenies in sage [sage] and in [magma].
 MR0294345, Jacques Vélu, Isogénies entre courbes elliptiques. C. R. Acad. Sci. Paris Sér. A-B 273, 1971.
 MR2695524, David Kohel, Endomorphism rings of elliptic curves over finite fields. Thesis (Ph.D.), University of California, Berkeley. 1996.
 MR2398793, Bostan, A.; Morain, F.; Salvy, B.; Schost, É. Fast algorithms for computing isogenies between elliptic curves. Math. Comp. 77 (2008).