Not at all! I'm new at this, so let me see how well I can do this in just text:
Presumably, you have some sample, and you are interested in its sample mean. Assuming you've shown that you can use a t-test here (or the book tells you to do it), you now want to test the hypothesis that the true mu = 5, ie, H_0: mu = 5. I'm also going to assume your significance level is .05
If your alternative is right tailed (H_1: mu > 5), you want to find sample mean M* such that P(M > M*) = .05 if the true mu = 5. In this case, you transform both sides of that inequality into the relevant t-distribution:
P( (M - 5)/SE > (M* - 5)/SE ) = .05
Because (M - 5)/SE is t-distributed with n-1 degrees of freedom (usually, I'll talk more on this later),
P( (M - 5)/SE > tstat ) = 1 - pt(tstat)
where pt(tstat) = P (T < tstat). Here, you look up tstat in a t-table with the relevant degrees of freedom, and then find the associated probability. Note that some books look at the right tail and some the left, so be careful! Anyway, this is what you want to do:
1. Find a tstat such that P(T > tstat) = .05. (do this using a computer or a t-table)
2. Solve for M* in (M* - 5)/SE = tstat
Now, for a two-tail alternative, it's very similar except you split that .05 region on either side, so on one side, that P(T > tstat) = .025 now:
1. Find a tstat such that P(T > tstat) = .025. (do this using a computer or a t-table)
2. Solve for M* in (M* - 5)/SE = tstat
3. Your critical value is |M*|, and you compare if |M| > |M*|
Left-tail is similar to right-tail, except switch the inequality.
And of course, if your null hypothesis wasn't 5 but some other number, replace the 5 with that number.
A final note: When you talk about critical values, you are usually talking about the critical sample mean M*, so if you get a sample mean M that's beyond that critical M*, you reject, otherwise you fail to reject. However, if you've already got your t statistic, ie, you've done (M - mu_0)/SE, then you only have to compare to that 'critical' tstat, which can be found by looking it up in a t-table/on a computer.
Recall that t-distribution is used in cases where you know what you're estimating has a Normal distribution, but you don't know the true variance sigma^2. Instead of sigma^2, you approximate using the sample variance, but this introduces some bias (deviation from true variance, say) that luckily the t-distribution corrects for. However, you'd also expect that, with increasing sample size, your bias gets smaller. This is why as n increases, the t-distribution converges to the Z-distribution. Therefore, unlike the unique Z distribution, you actually get a separate t-distribution for every different degrees of freedom!
Degrees of freedom for a single i.i.d. sample of size n is n-1. It's used in a lot of other contexts, but I'm guessing you're interested in if you need it to calculate a critical value, and the answer is yes, because it determines the t-distribution you're using.
Hope that helped, and don't hesitate to ask for clarification!