Yes. Provided you know the standard of your motherboard. Motherboards come in various form factors. The most common are ATX and microATX. Any case that supports ATX motherboards will also support microATX boards. ATX cases are very easy to find and very common.
There are many other form factors but they are all much less common. Measure your motherboard or look in your motherboard to determine your motherboard form factor. If you have trouble looking up what form factor your motherboard is, post your motherboard dimensions.
My friend told me that it's very difficult to move the motherboard. Can I do this by myself even though I'm a total computer noob?
Yes you can.
Make sure you ground yourself on something metal occasionally.
You'll want to disconnect everything. You can keep the CPU and ram in but I would remove any expansion cards.
There are screws at various locations, remove them all. Then make sure the new board has those backing screws so you can line them up with the motherboard. Line them up, jiggle the motherboard into place and screw it in. Then just transfer all of the other components in.
I'm sorry I'm not that great at explaining things but if you have any trouble, it's easy to find a guide to building a computer on the net. Basically, you just need to know how to install the power supply, motherboard and expansion cards in your case.