If you are upgrading your computer with a new motherboard, I recommend you go ahead and insert the RAM and CPU. It’s easier to do this before installing into the case. Just be careful when pressing down the RAM into the slots, because you don’t want to accidentally break the motherboard. Also be careful to follow all manufacturer’s instructions on installing the CPU and heatsink correctly.
Your new motherboard should have several holes in it that are used for screws to mount the board to the inside of the computer case. What I’ve always done is set the motherboard inside of the case and lined up the holes I needed, then use a Sharpie or some other marker to put a mark on each hole. Once you have them all marked, you will need to take out the motherboard and install the anchor screws first.

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Now you can put the motherboard back in place and tighten it down. It’s so much easier to use a marker than take the motherboard in and out of the case until you figure out which holes you need to use. Just be careful not to over tighten.
It does not matter what order you connect the drive and power cables, so long as you don’t have the power supply plugged into any electrical source. The very last thing you should do is connect the electricity, otherwise you’re asking for trouble. When running the cables, try to keep them clear of any cooling fans or in any pathways that might obstruct airflow. Be careful not to bend any of the cables too much, either.
Next, you’ll want to connect the front panel of the case to your motherboard. At a minimum, this will involve connectors for the power button and hard drive lights, and sometimes you also have to connect USB and audio ports. It all depends on the type of case you have and the features involved, and there are too many thousands of combinations to go into any great detail here. Your motherboard manufacturer should tell you where to plug things in, and the board itself is usually labeled, although the print is very tiny. In the past, I’ve had to use trial and error to get the power and drive light cables connected correctly.
In the old days, it was a lot more work to hook up a motherboard because you sometimes had to make some tweaks just to get the speed settings correct. Nowadays, most modern motherboards let you do all this via the BIOS, which makes the process a whole lot easier.
When you turn on your computer for the first time, it should go into a BIOS menu where you set the date and time, then you should check over the drives, make sure the boot sequence is correct, and so on. If your motherboard’s BIOS has any built-in memory and hard drive testers, I suggest you run them to make sure your components are working properly. Doing so will save you a lot of trouble down the line.