My father died in 1976 and left me $1000.00 as a gift in his will, I only just recently found out about his death and this will. I had just retired from the Navy in 1976, my father and I were estranged (long story) and met only once in my life when I came home on "Boot Leave" after Basic Training in 1956. I would like that money, it's the only thing I will have or given to me by my father in my whole life, how do I get it without much expense or trouble?

You must be in your late 70s? If living family don't know how the assets were distributed and who the executor of the will was, you have to apply at the probate court nearest to where he died. They may charge a fee to get records out of archives after 37 years; it depends on the courthouse. That's just to find out if the will even WAS probated or not, and if it was, who the executor was, and what the final distributions were. Your $1000 would have been put into a special bank account to be held until you were deemed unlocatable, a time of about 3 years (I didn't look up Texas), after which it would go to the other heirs.
Since you know about the $1000, that means that someone has some knowledge or even a copy of the will. If a sibling got that $1000, I suppose you could ask for it, but not on any legal grounds.

Would a copy of the will showing that your dad was thinking of you be a good memento, rather than the money?