As Rusty has said, por lo menos is a direct translation for at least. Whenever you'd use at least in English you can substitute por lo menos or al menos.
As far as por lo que, Rusty is right, and I'll give an example of usage. I'd often translate por lo que simply as "because", "due to", "due to the fact that", or even "for"; all of which really mean the same as "for that which".
Por lo que fuera, pero tal parecía que la ira dominaba los pensamientos y las acciones de todos en la casa.
For whatever reason, it seemed as if anger dominated the thought life and actions of everyone who lived in the house.
Por lo que más quieras, no hagas X.
Whatever you do, don't do X.
Por lo que más quieras, no le digas nada de esto.
Whatever you do, don't tell him about this.
El arbolito estaba creciendo, por lo que era necesario una maceta más grande.
The little tree was growing, making a larger pot necessary.
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If you find something wrong with my Spanish, please correct it!
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