As indicated in the instructions, there are two stages to solving this puzzle: assigning names to the constellations, and assembling them into a starfield.
The first thing to notice is that the "total brightness" of a constellation corresponds to the total number of half-stars in the constellation, i.e. count each half-star as 1 and full star as 2. Next, notice that the total brightnesses of the 13 constellations correspond to the enumerations of the 13 names (ignoring spaces and punctuation), ranging from 4 (CNTV) to 12 (SHINY DIAMOND). Putting these together, each name can be written on a constellation, with one letter in each half-star and two letters in each full star.
A useful thing to know about constellations is that its stars are typically assigned Greek letters in alphabetical order, often in order of brightness. (Ignore the numbers for now.) This gives an ordering for writing in the letters of a constellation's name onto the stars. This means you can go ahead and write the names with unique enumerations onto the constellations with total brightnesses 4, 10, and 12 in the corresponding Greek alphabet order (α, β, γ, etc).
For the constellation MAMMOTH MTN. (total brightness 10), this results in writing MA on the α star and TN on the θ star. Likewise, for the constellation SHINY DIAMOND (total brightness 12), write HI on β, NY on γ, IA on ε, and MO on ζ. It turns out that these bigrams are all US state postal abbreviations; this allows you to uniquely assign the names to constellations so that every full star is a different US state:
The fact that each star corresponds to a US state, plus the color scheme of white stars on rectangular blue backgrounds, indicates that the starfield to be assembled is, in fact, the canton of the US flag, also known as the jack of the United States. It turns out that the left and right half-stars can be matched up to form all the remaining US state abbreviations. Conveniently, the numbers after the Greek letters are the same for matching pairs, which should help with assembly. Also, the largest constellation, MAMMOTH MTN., covers almost the entire rectangle of the starfield, so that's a useful place to anchor the assembly.
The next step is to take this ordered list of US state abbreviations and numbers (which haven't been used yet, other than to help match up the half-stars) and use the numbers to index into the full state names:
Most of the indexes in the penultimate row are too big for the length of the state name (or too small, in the case of MA 0). This is a nudge to ignore the short rows, and read across the long rows: "IndexIntoCapitalsReadShortrows". This instruction indicates that for the short rows you should use the state capitals in place of the state names (a star also often represents a state capital on maps).
Read across the short rows to find out what we're celebrating (in the final star, Boston—well, we're in Somerville, but close enough) with these 50 stars:
A Stellar Half-Century!
Happy 50th birthday, Denis!