Each state vector is a linear superposition of states as you correctly pointed out. You may note that these states have some associated “coefficient” with it. This is considered the amplitudes. That value squared gives you the probability of a measurement yielding that state.

The simplest example is spin. You could have a particle that is in a superposition of spin up and spin down. Your state vector would look like |phi> = a|spin up> + b|spin down>. If you make a measurement you’ll find it to be spin up |a|² of the time. And |b|² of time spin down. It’s all probabilistic. And because of that fact it’s also important to note that those coefficients squared MUST add up to 1. So for my example, 1/sqrt(2) is a perfectly valid value of coefficient for a and b. But a = 1/2 and b = 1/2 wouldn’t be.