Without knowing your exact situation any advice will be pretty generalized and in no particular order but here goes:
If it's being thrown away, presumably it's available for you to take for free (barring any municipal restrictions on taking trash, which do exist places). Meaning everything has the potential for making you money.
If you've been recycling metals you know you didn't learn everything overnight. Circuit boards are no different. You also know steel is cheaper than aluminum which is cheaper than brass which is cheaper than copper and that there's nuance to all of those. Circuit boards just add less common metals to the mix. Tin, lead, nickel etc... on the lower end. Gold, silver, rhodium, platinum etc... on the higher end.
This is a great reference, especially Ropeman's links to actual items discussed in the forum.
Personal computers are fairly standard and you'll likely encounter those. So learn what a motherboard, power supply unit (PSU), expansion/graphics/gold-finger card, CD/DVD drive, floppy drive, hard disk drive, random access memory (RAM) and central processing unit (CPU) are. RAM and CPUs are the most valuable items by weight you'll get from those. PCs are also good to repair and sell working if you want to go that route.
If you pull a circuit board out of something cheap it's probably not that valuable. If it's from something that looks expensive or that has to last a long time, there's a chance the board is worth more.