In Texas Holdem if 1 player sees the card that is being dealt to another player is he supposed to say? If so, is that card then shown to everyone and used as the burn card with the player getting a new card at the end of the deal?
Should they say? Yes, otherwise they have an unfair advantage that can influence the game. Effectively they have another piece of the puzzle, and while that piece may be irrelevant, it may not. This is as much a question of morals/ethics as it is for rules.
As for what happens if the player announces he or she has seen another's card, it depends on the cardroom/casino and also the point at which the card was seen. So some cardrooms/casino's or tours will rule that during the initial deal, no action having occurred, it will be a misdeal and the hand will be reshuffled and dealt again.
Other venues will have rules pretty much exactly as you described above, but often it will apply only if all players have received one card. The exposed card will be shown to all players, it will become the first burn card. All remaining players will be dealt to in the correct order, the player whom has had a card exposed will then receive the card that should have been the burn card. Action will continue as normal.
In Texas Holdem if 1 player sees the card that is being dealt to another player is he supposed to say?
There is no rule that supports that a player is supposed to say if they saw an exposed card, and on the same token no rule that says a player is not supposed to say when they saw a card exposed. However it is considered good poker etiquette to mention when a card is exposed during a deal.
If so, is that card then shown to everyone and used as the burn card with the player getting a new card at the end of the deal?
Yes, that is the common procedure.
It is important to note that this replacement procedure should only be done when it is dealer error and not when the player accidentally exposes their own cards.