Descartes is the only one, who really understood the problem. I know the world through my perceptions, but I do´nt know, if my perceptions are true. However, I know, that I perceive, and therefore I know, I exist, because I cannot perceive, if I do´nt exist.
But this does not solve the problem, whether the world exists, or whether my perceptions of the world are true. So if I wish to go further, I simply must rely on my senses, and see how long it takes me. In this way, scientists have realised, that colours do not exist, but there is a connection between the frequency of light, and my perception of colour. I also know, that people, who are not colour blind, agree upon the same name of colours, as I do (we all call green “green”, blue “blue” and so forth, but we do´nt know if our perception of “green” and “blue” are the same).
I this way, we can build a common picture of the world, and we can even use this knowledge to manipulate the world in our favour, by building houses, aeroplanes etc.
From a practical point of view, there is therefore no reason not to believe, that the world exists, and our perceptions are in general valid. But philosophical, we cannot get further than Descartes.