What should I prepare FOR Linux?
Like obligatorily?

This is a nicer way of asking so I think I can organize my ideas and answer the topic too.

Before and while you consider the points below you must analyze and research:

• Are you curious and interested in software that may provide you a better experience after you have set it up, and do you have some free time?
• The reasons to switch to Linux.
• What desktop environment suits you better. The differences in using the computer compared to the other system you're used to exist but they're not necessarily good or bad, it's a matter of personal preference.
• What distribution is more in line with your ideals, wishes and needs. For this the development and release models and in which desktop environment(s) they specialize is also important.
• It may not be easy to evaluate all of that but happily you can try a LiveUSB/DVD/CD.

What you should know:

• Understand partitions.
• Learn what a bootloader does at least to the point where you can configure GRUB to remove the usual XX seconds delay when starting the system.
• For dual-boot. Windows won't want to read the Linux file system. Linux will read NTFS but only if Windows has been shutdown properly before you try to access it (ok with Win8.0, with Win8.1 I had to disable hibernation completely). More GRUB...
• Drivers. Everything should work out of the box but pray for your graphics card support.
• Lack of common media file formats support due to patents, etc.
• Software availability: what exists and what's in the official and unofficial repositories + packages downloaded from the web for your distro (e.g. RPM, DEB, other). Lack of proprietary software you're used to, so you'll deal with alternative software and sometimes they're not as feature-complete. And when one closed-source version of that software or an alternative exists (even if freeware) for Linux the majority of distributions will "boycott" it.
• Issues? Sometimes you can ask in a forum or create a bug report, but prepare yourself to learn the name of some components and what they do and receive instructions on how to edit some lines in a file in an obscure location (after some terminal-fu of course).

Linux with Windows...

What does that mean? (Like about dual booting?)

As far as Linux itself ... Linux doesn't get as much vendor support, hardware drivers can be a little slow in coming. So if you were to get the latest and greatest new whatever - just released last week - it might not work as expected. If your hardware is all parts that have been available for a year or so then it should be fine. Now 10 year old equipment may be a different story ... older equipment is slower and has less RAM and so on, and many of the big name distros simply stop including drivers for "obsolete" hardware. Not that it is hard to find Linux versions designed for older equipment, but you will actually have to look for it.