Note that $h$ is just a scale parameter: $K_h(u) = \frac{1}{h}K(\frac{u}{h})$.
So for the Epanechnikov kernel

Consider what's going on at one particular value of $x$, $x_0$, say: you're simply taking a weighted average of the $y$'s:
$\hat{y}_0 = \bar{y}^{(w)}=\frac{\sum_i w_iy_i}{\sum_i w_i}$
The weights are set up so we weight the observations down as we move away from $x_0$, where the weight on $y_i$ decreases down to 0 when $x_i$ is $h$ away from $x_0$; the weights are given by the kernel function.
So for example if we take the mcycle
data from the R package MASS and choose $h=2$, then at $x_0=20$ we can calculate $w_i=\frac12 K((x_i-20)/2)$:

The points in this region with the corresponding weights are:
times accel K2(x-20)
52 17.8 -99.1 0.00000
53 17.8 -104.4 0.00000
54 18.6 -112.5 0.19125
55 18.6 -50.8 0.19125
56 19.2 -123.1 0.31500
57 19.4 -85.6 0.34125
58 19.4 -72.3 0.34125
59 19.6 -127.2 0.36000
60 20.2 -123.1 0.37125
61 20.4 -117.9 0.36000
62 21.2 -134.0 0.24000
63 21.4 -101.9 0.19125
64 21.8 -108.4 0.07125
65 22.0 -123.1 0.00000
Note that the $K_2$ values -- the weights -- are computed from times
but used as weights in the average of accel
. The points that are included in the average are shaded according to weight (the deep blue ones in the middle get more weight than the less heavily shaded points nearer to the bound of the kernel near 18 and 22)
If we apply those weights* on observations with $x$ between 18 and 22 (since outside that region the weighted points contribute nothing), and calculate the weighted average, that will be the fitted value at 20. In this case it comes out to -106.67 (marked in blue on the plot).
* (these don't sum to 1, which is why we divide by the sum of the weights)
We can then repeat this kind of calculation every place we want to have an estimate of the smoothed function.