At level 5 Fighters get the Extra Attack ability, allowing them to make more than one attack as part of an Attack action.
Haste also enables people to make additional attacks.
Do the extra attacks from Fighter lvl 5 and the extra attacks from haste stack?
Haste specifically says in its description:
That [additional] action can be used only to take the Attack (one weapon attack only), Dash, Disengage.... (PHB 250.)
So you're hasted: you Attack with your action, and Extra Attack allows you to make two attacks. Now you take another (full) action granted by haste, and choose Attack. But this Attack is not amenable to Extra Attack--you can only make one weapon attack with it. That's three attacks in total.
Related: Haste spell: what does "one weapon attack only" mean?
