Learn Spanish (Latin America): Necesito barrerlo con la escoba.

Because barrer is an infinitive (an unconjugated verb that ends in -ar, -er, or -ir). In Spanish, object pronouns like lo (meaning "it") can be attached directly to the end of infinitives to form a single word.

Can I put the lo before the verbs instead, like Lo necesito barrer?

Yes! When a conjugated verb (like necesito) is followed directly by an infinitive (like barrer), you have a choice. You can attach the pronoun to the end (Necesito barrerlo) or place it before the conjugated verb (Lo necesito barrer). Both are correct and mean the exact same thing.

How do I know whether to say barrerlo or barrerla when translating "sweep it"?

It depends on the gender of the specific thing you are sweeping. Here, lo is used because "it" refers to a masculine noun, such as el piso (the floor). If you were sweeping a feminine noun, like la terraza (the terrace), you would use la and say barrerla.