Learn Russian: Я хотел бы сам починить этот старый кран. - I would like to fix this old faucet myself.

Сам is an emphatic pronoun meaning "myself" (doing it personally, without someone else's help). You use себя when you are the direct object of an action (like "I accidentally hit myself"), but here сам simply emphasizes the subject who is doing the fixing.

How do we know which form of the emphatic pronoun to use?

It must agree in gender and number with the noun or pronoun it refers to. Here it refers to Я. Because the verb хотел is in the masculine past tense, we know the speaker is male, so we use the masculine singular form сам. A female speaker would say Я хотела бы сама.

Could сам be placed somewhere else in this sentence?

Yes, Russian word order is flexible. You will often see it right after the pronoun, like Я сам хотел бы.... Placing it right before the infinitive починить gives a slightly stronger emphasis to the fact that he wants to do the fixing personally.

Why is the past tense verb хотел used when talking about a current desire?

The combination of any past tense verb and the particle бы creates the conditional mood in Russian. While я хотел simply means "I wanted", adding бы changes the meaning to "I would like".