| p | q | ~ p | ~ p V q |
-------------------------
|   |   |     |         |
|   |   |     |         |
|   |   |     |         |
|   |   |     |         |

Under all the letters p put TTFF

| p | q | ~ p | ~ p V q |
-------------------------
| T |   |   T |   T     |
| T |   |   T |   T     |
| F |   |   F |   F     |
| F |   |   F |   F     |

Under all the letters q put TFTF

| p | q | ~ p | ~ p V q |
-------------------------
| T | T |   T |   T   T |
| T | F |   T |   T   F |
| F | T |   F |   F   T |
| F | F |   F |   F   F |

Under all the negation symbols ~ put the opposite of what follows it:

| p | q | ~ p | ~ p V q |
-------------------------
| T | T | F T | F T   T |
| T | F | F T | F T   F |
| F | T | T F | T F   T |
| F | F | T F | T F   F |

Erase what was under the letter that followed the ~
(You don't have to erase it, but it keeps you from
getting mixed up, because you don't use it again.
You can also just mark through them:

| p | q | ~ p | ~ p V q |
-------------------------
| T | T | F   | F     T |
| T | F | F   | F     F |
| F | T | T   | T     T |
| F | F | T   | T     F |

Under the V put F only between TWO F's, otherwise put T

| p | q | ~ p | ~ p V q |
-------------------------
| T | T | F   | F   T T |
| T | F | F   | F   F F |
| F | T | T   | T   T T |
| F | F | T   | T   T F |

Then erase the ones on each side of the  last column you filled in:

| p | q | ~ p | ~ p V q |
-------------------------
| T | T | F   |     T   |
| T | F | F   |     F   |
| F | T | T   |     T   |
| F | F | T   |     T   |

You teacher might want you to leave all those columns and not erase them.
But if so, I would line through them lightly.

The final answer is TFTT.

Edwin