You should search for small wireless USB dongle (receiver) and insert it into USB port of your laptop. You bought The dongle with mouse. Sometimes it is placed inside mouse on bottom side. See picture. A mouse driver is usually installed automatically in a while after the dongle is connected to PC. Logitech M310 Silver 1 Wheel USB RF Wireless Mouse Model 910 001675
For changing the batteries of logitech wireless.I guess a video tutorial will help you out rather than written instructions. Watch it to lean how to replace battery of the logitech cordless mouse ( Logitech MX 1000 Model). If you are having a different model please specify the details of your model.
If your mouse is no longer working, it may be something as simple as the batteries are dead. You can normally check this by turning the mouse upside down, there you should see a small notch where the battery compartment is. Take the batteries out replace with new ones, be sure they are installed the correct way. Once you do that you may see a light, that's assuming it's an optical mouse. If it still doesn't work then you may want to check the receiver plug, and make sure that it's connected in the USB port or the mouse port just depending on the type of plug it is.
Although you don't specify which model, since you posted under the "Logitech Cordless Mouse" heading, I assume you have a Logitech mouse. In my experience, even modestly advanced (e.g., cordless, >2 buttons, etc.) Logitech mice don't always play well with mouse & keyboard settings tools found in Windows' Control Panel. Mr. Freeman's suggested adjustment to the generic Windows mouse management settings might be adequate for now. However, you're always better off using software specifically designed for your product.
The program you need is called SetPoint, and it's the key to getting full use out of your mouse or other Logitech device. All versions of the SetPoint software, and drivers for Logitech products, are available for free download at the Logitech support website. Here's the link:http://support.logitech.com/software/setpointLogitech Support
You need to go to http://support.logitech.com/software/unifying and download the software, then install it. It will let you pair your mouse with your receiver, and will let you add a logitech keyboard too, if you wish. If you are using Linux instead of Windows search for a program called Solaar.
Answered from the easy chair on my Samsung Note 3.
Brute force I'm afraid. There is a hairline gap which makers say you might need a paperclip to open. I found fine bladed kitchen knife used carefully the only way to open mine.