find a confidence interval in a linear model problem

i'm trying to solve a problem that involve a linear model given its normal equations, and the errors have a normal distribution but i'm a little lost. the problem is about construct a 95% confidence interval to $$\beta_{1},\beta_{2},\beta_{3}, \beta_{1}-\beta_{2}, \beta_{1}+\beta_{2}$$

i was reading about confidence intervals and say that if you have a set of observations, and you have to create a confidence interval for a parameter $$\theta$$ , then you need to construct a new random variable $$h$$ that satisfice a couple of properties:

1. $$h$$ is a function of the observations and of the parameter
2. the probability distribution of $$h$$ , doesn't depend of $$\theta$$ or other parameters.

I'm so confused about how get that $$h$$ function. maybe i was thinking that

$$h= h(Y_{1},Y_{2},...Y_{N},\beta)= \varepsilon$$, specially cuz we now that errors have a normal distribution. But i'm really not sure, moreover i dont have the observations $$Y_{i}$$, just the normal equations. Can you explain me how to get that Confidence interval?.