Each character class lists their Hit Die. For example, a Rogue has a d6 hit die, a Fighter has a d10 hit die.
At first level you get maximum hit points adjusted by your character's Constitution modifier. A Constitution score of 8 or 9 gives you a -1 modifier, a Constitution score of 10 or 11 gives you a +0 modifier, a Constitution score of 12 or 13 give you a +1 modifier, a Constitution score of 14 or 15 give you a +2 modifier and so on.
So a Level 1 Rogue with a Constitution score of 14 (and therefore a Con modifier of +2) would have 8 hit points (6 from his class, plus 2 because of his Con modifier).
A Level 1 Fighter with a Constitution score of 8 (and therefore a Con modifier of -1) would have 9 hit points (10 from his class, minus 1 because of his Con modifier).
From second level onwards you roll to see how many hit points you get at that level. So when you reach second level you would roll a die to see how many hit points you get at that level. What die you roll depends on what class you take.
For example, if you are a 1st Level Rogue and decide to take another level of Rogue you would roll a d6 and add your Constitution modifier. If you are a 1st Level Rogue and decide instead to take a level of Fighter you would roll a d10 and add your Constitution modifier.
Does that help?
Olaf the Stout