Understand the Pythagorean Theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the other two sides ($a$ and $b$). This is expressed as $a^2 + b^2 = c^2$.

Draw a number line and mark the point 0. From 0, measure 1 unit to the right and mark it as point $A$. At point $A$ (which is at 1 on the number line), draw a perpendicular line segment upwards, also of length 1 unit. Let the endpoint of this segment be $B$.

Connect point 0 to point $B$. This forms a right-angled triangle with legs of length 1 unit each. Using the Pythagorean theorem:

The length of the hypotenuse $0B$ is $\sqrt{2}$ units.

With a compass, place the needle at 0 and open the pencil end to point $B$. This sets the compass opening to a radius of $\sqrt{2}$ units. Draw an arc that intersects the number line to the right of 0. The point where the arc intersects the number line represents the location of $\boxed{\sqrt{2}}$.