How did the mujahideen finally defeat the Soviets in Afghanistan?

The Mujaheddin were supported by financing from the US and Saudi Arabia among others. US Sanctions were a significant force on the Soviets and it is interesting that the Soviet regime in the USSR fell soon after the withdrawal. The war was typically brutal and there were high casualties among the guerrillas and civilians. Many people fled to Pakistan where they often raised new Mujaheddin to go back to Afghanistan.

Stinger missiles supplied by the US made some difference in the fighting after 1986 but there is some dispute about how much this was. Certainly they had some effect Soviet air power. Sanctions, intractable warfare, and internal Soviet problems were major reasons for the withdrawal of the Soviets.

The Mujaheddin were supplied with Chinese made heavy machine guns and other Soviet style weapons (RPGs, AK 47s, mortars). They made ambush attacks that tried to destroy convoys and minor fortified areas to choke off the transportation corridor. They would disappear into the rural areas afterward. Casualties were replaced fairly quickly from locals or from returning refugees from safe havens in Pakistan. A very textbook rural guerrilla war. The brutality of the Soviets helped motivate the individual Mujaheddin.

The Soviets made extensive and indiscriminate use of mines both directly buried and scattered by aircraft as an area denial weapon. The Soviets also brutally attacked villages and rural areas to combat the guerrillas. The Soviets were defending Kabul and a transportation corridor and not much else. The Kabul Government had limited effect outside of Kabul.

The Taliban created a stable Islamic state in the 1990s which became a haven for Al Qeada.

https://en.wikipedia.org/wiki/Soviet%E2%80%93Afghan_War#1986:_Stinger_Missile_and_"Stinger_effect"