Each level, you get Hit Die + Constitution modifier additional Maximum HP. You always take the maximum of the Hit Die at 1st level; afterward, you may roll the Hit Die or take its average rounded up.

Therefore, with a 1d10 Hit Die and +3 Constitution modifier, assuming you take 6 each time instead of rolling:

\begin{array}{rrcrcrcr} \text{1st level:} & 10 & + & 3 &&& = & 13 \\ \text{2nd level:} & 6 & + & 3 & + & 13 & = & 22 \\ \text{3rd level:} & 6 & + & 3 & + & 22 & = & 31 \\ \text{4th level:} & 6 & + & 3 & + & 31 & = & 40 \\ \end{array}

In short, you will add 9 HP for each level beyond 1st.

If your Constitution modifier later changes, it will apply the new bonus for every level you had so far. So if at level 4 your Constitution modifier is boosted to +4 instead of +3 (for a difference of 1), you will add 4 HP because you are level 4, which will make your HP 44 instead of 40. (It's basically as if your Constitution modifier were +4 all along.)

Max at first level

Page 23 of the Player's Handbook states:

For his or her first Hit Dice, a 1st level character gets the maximum hit points rather than rolling.

Since you were not rolling your hit points in the first place, the amount of hit points you gain at first level does not change.

Note: There is no reference to this on the d20srd (that I could find), I believe this is because character creation information is not covered by the OGL.