The "PLAI" book explains how to do it trough a rewrite/desugaring transformation: [0]

    The heart of [a CPS] transformation is [...] to turn every one-argument function, f, into one with an extra argument. This extra argument is the continuation, which represents the rest of the computation. The continuation is itself a function of one argument. This argument takes the value that would have been returned by f and passes it to the rest of the computation. f, instead of returning a value, instead passes the value it would have returned to its continuation.

    CPS is a general transformation, which we can apply to any program. Because it’s a program transformation, we can think of it as a special kind of desugaring: in particular, instead of transforming programs from a larger language to a smaller one (as macros do), or from one language to entirely another (as compilers do), it transforms programs within the same language: from the full language to a more restricted version that obeys the [... CPS pattern]. As a result, we can reuse an evaluator for the full language to also evaluate programs in the CPS subset.

There's a more terse description on this site too [1]. And I have to agree with this:

   [...] there are many methods for transforming into CPS [... but] learning CPS transformation remains difficult.

Also I remember stumbling upon this article [2] which kind of gave me an excuse to not pay too much attention to CPS :-) (...but not really :-p, mostly the subject got too hairy for me and I lost interest :-p). If I remember right, the article argues in favor of "delimited continuations" as opposed to implementing full general call/cc.

0: http://cs.brown.edu/courses/cs173/2012/book/Control_Operatio...

1: https://matt.might.net/articles/cps-conversion/

2: https://okmij.org/ftp/continuations/against-callcc.html