Learn Russian: Перейди дорогу здесь.

This is a direct, one-time affirmative command to get a result (cross it completely). For positive commands like this, Russian usually uses the perfective aspect.

How would this sentence change if I wanted to say 'Don't cross the road here'?

You would add не (not) and switch the verb to its imperfective partner, переходи. The sentence would become Не переходи дорогу здесь. Remember the current lesson's rule: affirmative commands generally use the perfective, while negative commands (prohibitions) use the imperfective.

What is the infinitive of перейди and how do we get this imperative form?

The infinitive is перейти (to cross on foot). To form the imperative, we look at the 'I' form in the future tense: я перейду. We drop the ending (-у) and add -и, giving us перейди.

Why does the word for road end in -у (дорогу)?

Дорогу is the direct object of the action (it is the thing being crossed). Therefore, the feminine noun дорога changes its ending from -а to -у to show the accusative case.