intro. A stream cipher encrypts bits individually

For the $i$th bit:

encrypt: $y_i = e(x_i) = x_i + s_i ~\mathrm{mod}2$

decrypt: $x_i = d(y_i) = y_i + s_i ~\mathrm{mod}2$

why it works, because mod(2) addition and substraction are the same operation! (it is also the same as XOR (see Modulo 2 arithmetic)

how do we generate the key, which has to be shared between sender and receiver (Symmetric cryptosystem). They should be random, using a Random number generator

The One time pad is an Unconditionally secure stream cipher