For the inexperienced
One word: Don’t.

Unless, of course, you will be exactly following the advice of an expert or copying something you have seen that works well.  Even then do not make modifications to save money.  Example, (at the time of writing), vortex £200, dustbin £20, therefore you save £180. Wrong!  A vortex is that particular shape because it has to be. A dustbin will not do the same job as efficiently. The dustbin may also be made of a type of plastic that will leach toxic chemicals into the water.  You may soon have to take your £180 “saving” and buy some new fish, and a proper vortex.

For the experienced
Koi keeping is a hobby.  Hobbies are supposed to be fun. If you gain more pleasure from saying, “I built that” than you do from saying, “I bought that” then you will probably want to build your own filter system. Few koi keepers have an unlimited budget to spend on their hobby so sometimes the only way to add a particular feature, such as a protein skimmer or trickle tower, and not exceed your budget, may be to build it.  The savings can then be spent on better quality fish or squandered on household bills.