I have a Lenovo computer with an intel core i-4440 CPU @3.10 GHZ can i upgrade the cpu and if so how do i get the right one?

For the money it doesn't pay. CPU's have "sockets", which is a fancy name for the plug. Each new generation has a new socket. You will be able to buy something more powerful, most likely, but nothing like later generations. And whatever you do it will be on an obsolete motherboard, too. I'm typing on a refurbished i5 desktop I bought from a certified refurbisher on Ebay for $179, free shipping. I got an i7 the same way for under $800. Those are about $1200 at Best Buy right now.

Hmm… Lenovo does not provide that information on their web site. (Unusual in my experience - typically companies list which CPUs work with their systems.)

Probably just about anything that uses the FCLGA1150 socket will work in your PC… But I can't be sure because manufacturer's BIOS also needs to support a CPU for it to work properly.

My advice: contact Lenovo and ask them which CPUs work with your model. (You'll need the model number and perhaps also the serial number.)