The most time efficient way to sort the wheat from the chaff is hard to gauge, there are a number of different ways that will work for different people.
One option is to take a buylist from your preferred website, which will give you prices for most cards that are valuable. This lets you quickly look through a list of cards (often sorted in alphabetical order and set) all in one place, and check if its on the list.
This wont give you the ACTUAL value of your cards, but generally a buy list price indicates whether a card has much value.
many websites will also let you type in a list of cards and bring up their sale prices of each, which might be quicker depending on how quickly you can go through them.
a further option would potentially be a mobile app, many apps have collection trackers where you can enter your entire collection and then traverse the list in the app to get values for them.
whatever you choose, it will probably be pretty time consuming. Rather than going through your cards and comparing them against the web or a list, it might be better to try and learn as many commons and uncommons worth more than a specific threshold (e.g. $1) as possible, and then go through your collection looking for those specific cards, seperating out any rares and foils to check later. While there are plenty of commons and uncommons that are worth money, there arent so many that you cant have a good idea of what most of them are. having a threshold as low as $1 makes it significantly harder, but starting at $5 cuts out a huge number, and gets you most of the value in your collection quite quickly, before making further passes to pick out the rest, knowing you dont need to look for anything above $5.