You can have up to 16 GB RAM in that system. If you want that much, ideally you should install a matched pair of two identical 8 GB sticks. If you currently have a single 8 GB stick in one slot (since you said that you want to "add another 8GB RAM"), you could try installing an 8 GB stick in the other slot. However, sometimes mismatched RAM brands/models may not play well together. Crucial shows compatible RAM for your system. You don't have to buy from Crucial, but they will accept returns and refund your money if the RAM doesn't work in your system. If you buy elsewhere, you may want to look for such a guarantee. I recently bought a relatively unknown brand, Kuesuny, through Amazon for much less than the price of a big brand name, and I'm happy with it. I ran memory tests for a couple of days to thoroughly test the RAM when I first installed it. It performs well and saved me money. Replacing your spinning HDD with an SSD will make it much faster and more responsive, a noticeable difference and the most bang-for-your-buck that you can get for any upgrade. I recently bought a Crucial Mx500 1TB SSD for about $100 Canadian. And, you may not even need that much storage. I highly recommend that upgrade as a way to speed up your system. You could use a drive imaging utility such as Acronis or Macrium to backup the HDD and restore to the new SSD (after installing it). But, I recommend that you install the SSD and perform a clean install of Windows. That will yield a superior result. Follow the disassembly and reassembly steps in Dell's Service Manual.Look on YouTube for videos showing disassembly of your model. But, be cautious with them, as some use steps or methods that are not appropriate. Use the videos to add to your understanding of what to do, but follow the steps in Dell's manual. 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.
I am keen to add another 8GB RAM to my system and also want to mount an SSD drive along with the exiting HDD. I have been through some forums where they suggested that the following upgrades might be possible, however, I think there is no way to change the processor. The current intel i5 8th gen has a clock speed of 1.6 GHz which is pretty slow, so I am not sure if changing the RAM and mounting additional SSD would make it work any faster ! Any suggestions ? 
Upgrading Dell Vostro 3578 processor