If I am a permanent resident in the USA, how can I get my fiance into the USA?

You cannot petition for a fiance as a green card holder. However, if you marry, you can petition for your spouse even if you are a green card holder.

Lawful permanent residents cannot petition for fiances. Thus, you have to be legally married before you can file an I-130 petition on his behalf.

Only US citizens can file fiance petitions. But as a green card holder, you can file a Form I-130 petition which requires that you have to marry him first. Processing of I-130 petitions under F1 (immediate relative of a legal resident) takes about 6 months.

Only U.S. citizens can file a K-1 fiancee visa which would allow the fiance to join him/her in the U.S. for the purposes of getting married. As a legal permanent resident (LPR), you would have to get married before you could file a petition for your spouse. Also, a spouse of an LPR does not have a visa number immediately available to him/her, so there would be a significant wait time. How long before you are eligible to naturalize? As a naturalized U.S. citizen, you would have the option to file a K-1 fiancee visa.