Dell Lattitude E6420 RAM Upgrade

You didn't say whether your laptop has a hard drive or an SSD. If it's a hard drive, replacing it with an SSD will make a much bigger performance difference than upgrading to 16 GB RAM. An SSD will make it much faster and more responsive, a noticeable difference. Crucial's MX500 SSDs have recently been reduced in price. They are good performance and good value for the price. You could get a 500 GB for less than USD $50 or a 1 TB for less than USD $80.

Unless you routinely work on large images or videos, or some other high-memory task, 8 GB RAM + SSD will be a much better investment than 16 GB RAM.

JOcean is correct. You need DDR3 SDRAM (1333 MHz). Crucial shows guaranteed compatible RAM up to 8 GB. But, since you have a 2nd-gen i7 CPU, you should be able to use 2 x 8 GB for a total of 16 GB, though as I said that may be more than you need. Whatever you buy, buy a "kit", which is a matched pair of identical RAM sticks. That will make success more likely.

You don't necessarily need to buy RAM from a big brand such as Crucial. I recently upgraded my 2nd-gen i7 laptop with Kuesuny RAM, bought from their Amazon store. They use well-known memory chips such as Micron and Samsung. They have lifetime warranty and their support is responsive to emails. I tested mine by running memtest86 for several days. I'm happy with the RAM and it was cheaper than Crucial.

As your laptop is 11 years old, then the thermal compound has dried out and is cannot adequately transfer heat away from the processor, and there may be a lot of dust inside the laptop and maybe inside the fan and heat fins. So, your laptop is unable to adequately cool itself.

You might consider an internal cleaning. Open it up to clean out dust. Disassemble the fan to clean out dust and fluff. I found a fair bit in two laptops I worked on recently. Remove the heat sink, remove the old thermal compound and apply new thermal compound before reinstalling the heat sink.

While you're in there, replace the CMOS battery. If it isn't dead, it soon will be. BIOS settings and date/time can't be saved without a functioning CMOS battery.

Here's the Dell service manual for your laptop. You will also find YouTube videos showing disassembly and parts replacement 

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. I know many people do such work without this, but it's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard.