This is probably a trivial question, however I'm unable to select a given color in Photoshop. I'm using a template in PSD which is set to CMYK and I think that this is the problem.
For example if I try to assign a text the color #00FFFF it automatically sets it to #6FCCDC instead of converting it to CMYK. How can I have the color properly converted so that it looks like a #00FFFF also when printed in CMYK?
... if I try to assign a text the color #00FFFF it automatically sets it to #6FCCDC instead of converting it to CMYK.
It is converting it to CMYK...
CMYK and RGB have a different gamut, so converting from one to the other will result in color changes. The hexadecimal colors you have there are an RGB notation, so if that color doesn't exist in the CMYK gamut you're converting it to then it has to change.
What doesn't help any of this is the fact that Photoshop's color picker shows you RGB colors regardless, so a bunch of the colors you see in the color picker aren't even available to you in a CMYK document...
Two things...
If you have a color that is "out of gamut", the color picker will show you a little warning triangle to the right of the color (with Photoshop's closest available match underneath), you can click that to get that in-gamut color.
Another thing you can do; with the color picker open, go to View → Gamut Warning. That will grey out any colors that are out of gamut... you then simply only pick colors you can actually see in the color picker and you won't get any nasty surprises with color changes.
How can I have the color properly converted so that it looks like a #00FFFF also when printed in CMYK?
You can't. That color is very far from what is possible with CMYK printing. You can use special inks (e.g. Pantone) but that is a whole other subject...
