Alright, so let's say you have this problem:
$$x = -2\text{ and }x = 3\\ y = \begin{cases}2x + 3 & \text{if }x < 0\\ 2x + 5 & \text{if }x > 0 \end{cases}$$
So do you look at the if statement, then plug it in if $x$ works? For example, for the first condition, I look at $x < 0$. Do I only pick out $-2$, because it's only true for that, then solve? That would make my final answer $f(-2) = -1$, correct?
OR...
Do I plug all of them in, then write the solution if the final answer applies? I'm really confused someone please help me.
Yes you check the condition on $x$ and use the formula that applies. By the way, your function is not well defined in general since it doesn't specify what happens if $x=0,$ but maybe you want $(-\infty,0)\cup (0,\infty)$ as your domain. Assuming you didn't want to include zero $$ f(x)=\left\{\begin{array}{lcl} 2x+3, &\mathrm{ if } & x <0 \\ & & \\ 2x+5 &\mathrm{ if} & x> 0\end{array} \right. $$ So $f(-2)=-1$ and $f(3)=11.$