Hi Lieven,
Some people advocate replacing strings one by one but I prefer to remove all the strings so I can give the whole guitar, especially the fretboard, a good clean.
There is a way of fitting your strings and locking them so you do not have to have it wrapped round and round several times and it will stay in tune better this way. It is not easy to explain in words but I will try.
To start you need to have the hole through the machine head in line with the string. Fasten the string at the bridge end and feed it, in it's locating grooves, straight through the hole keeping it fairly taut. Without letting it slacken off wrap the spare end around the around the machine head in the opposite direction that the machine head will turn it to tighten the string, take it half way round and under the string and then pull it back in the opposite direction. When you tighten the string it will wrap over the spare end and trap it making it very secure. The excess string can then be cut off and when all strings are fitted then you can tune it.
Done this way it only takes about half a turn of the machine head to tune the string.
Roger
PS I have sent you a diagram by private E-mail which should help if you want to try this way.