What is RAM?
Random Access Memory (RAM) is a type of computer memory that is able to be accessed randomly by the operating system and active applications. When a computer boots up, data for the operating is loaded onto the RAM to be accessed when needed. This same process is used when other applications are run. This is why the quality and performance of your RAM is integral to the performance of your PC.
What RAM do I need?
The type of RAM you need is mostly dependant on whether you have a laptop or desktop, but there are some other factors involved when picking out your memory.
If you're building or replacing RAM in a desktop, you'll most likely need DDR3 DIMM RAM. However, DDR2 RAM is a legacy type of memory that is still found in some systems, so if you're replacing or installing more RAM, be sure you know what type you have. DDR4 RAM is a newer memory type which is starting to gain notice and popularity, but is still mostly just used by private system builders. If you want to build a system that is on the cutting edge, you'll likely need to get DDR4.
Laptops are a little different in that they just can't fit DIMM modules, but instead require SODIMM modules (the "SO" stands for "small outline"). SODIMMs are simply the little brother of DIMM modules, and perform the same functions with effectively the same performance. You'll be a bit more hard pressed to find anything but DDR3 in a laptop anyone is using today, but there are still some running that use DDR2.
How much RAM do I need?
For most users, 4GB to 8GB of RAM is plenty, but gamers and performance enthusiasts will often install between 16GB to 32GB or more to make sure their system has as little slow-down as possible while they're playing online, recording game footage, overclocking, rendering 3D models, or other hardware intensive functions. For professional level users who use software that requires it, you may need 64GB or more for your application.
Most computers today run on a 64-bit system, but some are still 32-bit. The big issue here is that 32-bit systems are only able to support up to 4GB of memory. It's mathematically impossible for them to run any more than that. However, most 64-bit systems support 16GB if not more. For instance, Windows 7 Professional caps supported memory at 128GB.
What limits how much RAM I can install in my system?
There are several limitations to the amount of RAM you can install and recognize in your system. First - the physical number of RAM slots you have available to you. Most laptops have 2 slots for memory and most desktops have between 4-8 slots. You can install memory into available slots in accordance with your slot availability. It should be noted that different motherboards may restrict slot usage based on the channel configuration required (such as Single / Dual / Triple / Quad Channel) so you always want to read your motherboard manual to see how you will be using the system. Different chipsets, processors, and/or motherboards will have limits to the maximum memory recognized per memory slot. For example, if you have 4 memory slots and each can accept up to 8GB in a single stick, you can install 4x8GB = 32GB total. Again, refer to your motherboard specifications for information on this. Lastly, you'll want to make sure your operating system can actually recognize the amount of memory you physically have installed. This is particularly important if you are using a 32-bit operating system as those have limitations on addressable memory up to nearly 4GB. What that means is that any memory installed in your system past that amount simply won't be usable to you.