Portfolio beta is calculated by weighting each position's beta by its share of capital and summing. Short positions enter with a negative weight.
Example on $100,000: $30,000 in a 1.4-beta name, $40,000 in a 0.9-beta name, $20,000 short a 1.2-beta name, $10,000 cash. Weighted beta = (0.30 x 1.4) + (0.40 x 0.9) + (-0.20 x 1.2) = 0.42 + 0.36 - 0.24 = 0.54. The book should move roughly half as much as the index.
Compare that figure to your intent. Many traders who believe they are neutral find a beta near 1, and many who feel aggressive are effectively flat. The number also tells you the size of the index hedge needed to neutralise: 0.54 x $100,000 = $54,000 of short index exposure.
Related: beta, beta-weighted-delta, net-exposure