Here we'll be studying x86 and x86-64 architecture registers, following mainly Intel Pattern. In order to store data in general, the main "thing" we use are registers.
At x86 architecture there are eight 32-bit general purpose registers (GPRs), some of them can also be divided into 8 and 16-bit registers.
16 - Bits
Acumulator, used for arithmetic operations and to store results
Base register for the stack
Counter in loops
Used to store addresses of the data
16 - Bits
Source in string/memory operations
Destination in string/memory operations
Base Frame Pointer
16 - Bits
Instruction Pointer (Program counter)
Store operations - Ex: Flag Zero
The x86 instruction set are around the data movement between registers and memory, classified in 5 types:
Immediate to register
Register to register
Immediate to memory
Register to memory and vice versa
Memory to memory - Only in RISC architectures.
The focus here will be the Intel syntax. AT&T prefixes the register with % and immediates with $, which doesn't happen at Intel. They also add a prefix to the instruction to indicate operation width (long, byte, etc.). At Intel syntax the destination come and then the source (op dest source), at AT&T it is the opposite. Instructions have variable-lenght (1 to 15 bytes).
x86 uses  to indicate memory access (similar to * at C/C++) In order to sum or subtract address inside  usually is used hexadecimal, for example: mov eax [ecx+10h] - Where the h is used to indicate hexadecimal notation.
MOV - mov ecx, [eax]
Sets ecx = [eax]
ADD - inc dword ptr [eax]
Increments value at address eax.
SUB - sub eax, 0x20
Subtracts eax by 0x20.
PUSH - push eax Pushes eax at the stack
CMP - cmp eax, ebx if(eax == ebx) Sets eflags;
JNE - jne 0x400086 Jumps to given address if eflags was set to equal.
CALL - call 0x400086 Jumps to given address and saves current location at stack.
RET - ret
Pops the address of the stack and returns control to that location - ("jump").
LEA - lea eax, [esp+0x1c]
Moves address of register to another (eax = esp+0x1c), used to pass parameters
LEAVE - leave
Moves ebp to esp and pops ebp from the stack.
Load Word -
LDR R3, [R3]
Read the value at address R3.
Store Word -
STR R2, [R3]
Store the value from R2 at address R3.
Add to register -
ADDS R2, R3, #1
Add 1 to R3 and store at R2.