Assess the dish carefully to determine whether it can hold up with tomato puree rather than diced tomatoes. If you are making a fairly wet, liquid dish -- such as a stew, chili or soup -- chances are you can substitute tomato puree for diced tomatoes successfully, though the texture and flavor of the final dish will probably be noticeably different. If your recipe relies on the texture of the diced tomatoes, however -- such as in the case of salsa -- you should not make the substitution.
Measure out an amount of tomato puree equal to the amount of diced tomatoes required in the recipe you are making.
Add the tomato paste to the recipe well before you would have added the diced tomatoes canned. The tomato jam can handle long cooking times much better than diced tomatoes, which would crumble and disintegrate. Cooking the tomato paste for longer will help incorporate its flavor into the rest of the recipe.