Drawing a number line can help students understand that numbers aren't real entities; they're representative of a quantity. It's impossible to have a 2, just as it's impossible to have a negative 2. Instead, you can only have two of something. Showing negative numbers on a line demonstrates that, whenever a person has less than zero of something, she has a negative quantity of that item.
Negative numbers are another way of doing subtraction. Understanding negative numbers as a form of subtraction can help students understand operations with negative numbers. For example, explain that negative 2 really just means subtracting 2, so if you add negative 2 to a whole number, you can still end up with a quantity higher than zero. When students understand negative numbers as a form of subtraction, they're less likely to be confused by the fact that negative numbers are abstract entities.
Giving students real-life exercises during which they can learn about the relationship between negative numbers and subtraction helps make the concept more relevant and concrete. Try giving students 10 pennies. Then ask them to "spend" two pennies, and explain that the two spent pennies are an example of negative 2. Then ask a student what happens if she spends 11 pennies. She'll respond that she can't because she only has 10 pennies. Explain that this means she needs 11 pennies to get back to 10, which means she has negative 1 pennies. Another way of explaining this is to have students "owe" other students pennies. When they've spent all their pennies and still owe money, the negative quantity represents the amount they have to pay to get out of debt to the other student.
It's likely that students already use negative numbers in their daily lives, perhaps without noticing. Giving students several examples of real-life negative numbers can help the concept become more relevant. For example, point out that negative numbers are relevant when the temperature falls below zero, when a person spends more money on her debit card than she has or when a person digs below the surface of the earth and is a certain number of negative feet below sea level.