Adding AWGN noise with certain power
This is solved slightly differently if you're simulating a continuous-time or discrete-time AWGN channel. I'll assume you're simulating a discrete-time channel; that is, you're simulating the output of the receiver's matched filter sampled at correct time instants.

First consider the case with no noise. In this scenario, the matched filter's output is an array of numbers, each of which is equal to $+\sqrt{E_b}$ or $-\sqrt{E_b}$. The average energy per sample is then equal to $E_b$.

Now consider the case where only white noise is present at the matched filter's input. The sampled filter output is a sequence of random values with variance $\sigma_n^2$. The signal-to-noise ratio is defined as $E_b/\sigma_n^2$. By convention, $\sigma_n^2$ is denoted $N_0/2$, which means that $\text{SNR}=2E_b/N_0$. (This is because when the filter input is white noise with power spectral density $N_0/2$ and the matched filter's impuse response has energy equal to 1, then the variance of the sampled filtered noise is also $N_0/2$. This is a technical detail that you may omit for now and come back to when you're more comfortable with the theory).

Then, $$\sigma_n^2=\frac{N_0}{2}=\frac{E_b}{SNR}.$$ Using this equation you can easily simulate any SNR you want. A word of caution: it is common, when plotting the bit error rate vs the SNR, to use $E_b/N_0$. Be aware of this when comparing your results to those published elsewhere.