Starting with the feminine rueda, you can listen to its pronunciation here:

You’ll usually find four ruedas on a car, two on a bicycle and one on a unicycle, as they are the wheels that roll along the ground allowing it to move backwards or forwards. Una rueda can also be a wheel in a mechanism.
La invención de la rueda fue más importante que cualquier acontecimiento político.
The invention of the wheel was more important than any political event.
una rueda oxidada
a rusty wheel
Poco a poco la rueda hidráulica se fue aplicando a varios usos.
Gradually the water wheel started being applied to different uses.
By extension, una rueda can also refer to a tyre, the air-filled covering found on vehicle wheels:
He tenido un pinchazo lento en una rueda delantera.
I had a slow puncture in a front tyre.
Una rueda can also be a ring or circle of people or things:
Se fue formando una gran rueda de oficiales y soldados en torno al capitán.
A large circle of officers and soldiers was forming around the captain.
El alcalde ha convocado una rueda de prensa para hoy a mediodía.
The mayor has called a press conference for noon today.
Moving on to the less common ruedo (masculine), you can hear how it is pronounced here:

Un ruedo is also a ring or a circle, but in rather different contexts.
It may refer to a bullring (or an arena), the area surrounded by fencing and seating where bullfighters ply their trade:
Los toreros entran en el ruedo.
The bullfighters enter the (bull)ring.
Ruedo can be used figuratively as an arena too:
Ha vuelto al ruedo político en Argentina.
She’s returned to the political arena in Argentina.
El joven escritor se lanza al ruedo con su primer libro propiamente dicho.
The young writer is throwing himself into the ring with his first proper book.
DID YOU KNOW?
Both rueda and ruedo are related to the verb rodar, whose primary meanings are to roll and to film. Unsurprisingly, given the spelling of the related nouns, rodar is a radical changing verb, with the roots of the present indicative and present subjunctive affected:
Los automovilistas ruedan a velocidades que hacen imposible el frenazo.
The drivers travel at speeds that make braking impossible.
La mayor parte de los episodios se ruedan de noche.
Most of the episodes are filmed at night.
To see where we roll up next time we put Spanish nouns under the microscope, come back next week.