For a Yagi antenna the electrical polarisation matches the mechanical orientation of the elements. So to receive your vertically polarised signals the elements of your antenna will need to be vertical (i.e. up and down).
It does indeed seem tricky to find a clear illustration of this via Google. Wikipedia does have a clear illustration of how the electric field interacts with a half-wave dipole. It shows how the electric field is aligned with the dipole elements. This picture shows horizontal polarisation.

Source: Wikipedia
A Yagi-Uda antenna uses a half-wave dipole as the driven element. The directors and reflector are in line with the driven element.
The polarisation of a radio wave is always specified as the polarisation of the electric field component of the wave. A radio wave also has a magnetic field component which is at 90° to the electric field (omitted in the picture above). So a vertically polarised radio wave will also have a horizontal magnetic field.
Source: Wikipedia
In the picture above $ \vec {\mathrm{E}} $ represents the (vertical) electric field,
$ \vec {\mathrm{B}} $ represents the (horizontal) magnetic field and z or $ \vec {\mathrm{V}} $ represent the direction of propagation of the radio wave (travelling towards the right of the picture).
The arrows over the variables indicate they are vector quantities - that is, they have both a magnitude, shown for $ \vec {\mathrm{E}} $ and $ \vec {\mathrm{B}} $ by the length of an arrow, and a direction, shown by the direction of the arrow.
(Note that this diagram is a graph of the electric and magnetic field strengths and directions at points along the direction of propagation (the z axis) shown in the picture. If this was visible light we would call this a ray. It is not a picture of what a radio wave would look like if the fields were visible.)