If you want to learn how to play, see Tutorial.
You've now learned how to play, and you have a nation under your control. Obviously things may be slightly confusing to you.
Ways to improve your approval rating slightly.
Yes, you can appear in public. At a video game competition, army barracks, or at a university. Simply go to national policies menu (next to foreign policy) and you can boost popularity slightly. Or get shot by an angry citizen.
Furthermore, during times of war visiting a barracks makes sense, if unemployment is falling or you have boosted employment assistance visit a employment job provider. If education is your thing visit a university, if you want law and order to be a focus visit a police station and same day announce increase in police numbers.
Only meetings with leaders of wealthy countries known for a decent human rights record at home (e.g. Canada, Germany, Australia, Japan, France, United Kingdom, Spain, Italy, Sweden, Norway, The Netherlands, Switzerland, New Zealand) count for this one to increase popularity, while meeting with the leaders most countries have no bearing on your popularity and your popularity will suffer from meeting with the leaders of countries including, but not limited to China, Sudan, Kazakhstan, North Korea, Iran, Russia, Pakistan, Libya, Brunei, Cuba and Saudi Arabia.
Under "Research" you can view your country's national scientific discoveries. As a universal rule, patenting or publishing anything related to the military will destroy your popularity, but you can also increase your popularity by patenting or publishing discoveries that aren't military related, such as space technology and civilian aircraft.
You can also increase your popularity by having meetings and then awarding the national medal to your nation's celebrities (artists, athletes and intellectuals) and to a lesser extent syndicates, associations, institutions, other parties, servicemen and religous leaders.