Immerse yourself in the local culture. Liberia has a thriving music scene, known as hip co, which blends hip hop with colloquial Liberian English. Artists like Takun J, Santos, Mr. Smith, Soul Smiter, and Nasseman are popular. In the dry season, especially, concerts are regularly held at venues across the country.
Liberia also has several nightclubs. While places like Deja Vu cater to a largely expat crowd, explore places more popular with locals. 146 on Carey Street features Liberian music, freestyle sessions, and live performances from Liberia's most popular musicians.
Almost every international NGO operates in Liberia. It is very possible to find voluntary unpaid work here, if you are willing to stay for a bit. Paid work is almost exclusive through international organisations. Most of these organisations require foreign staff to be recruited abroad, so it is unlikely that you would be hired just because you managed to make it to Liberia.
Liberia has very high rates of unemployment. If you are in the country for longer, try to encourage local production and employment by buying local goods and paying for services.
Liberia has just come from devastating war, so the learning curriculum is not at its greatest. As a tourist personally, you can learn about many attractions in Monrovia. You can personally learn a lot about Liberia's culture, art, design, etc. It would be easy if you associated with trusted foreigners to give a personal tour and as a tourist, you can learn about this interesting historical country.