I'll take a crack at trying to explain this, but it's up to DNZ to correct any mistakes, go more in-depth, add things I forgot, post links to other threads, etc.
The question of a revolution in a third-world country, where the proletariat represent a minority of the population, is especially hard. Many have proposed different solutions to the problem, such as advocating permanent revolution, new democracy, the joint dictatorship of the peasantry and the proletariat, etc. but Third-World Caesarean Socialism sees the itself as a solution beyond permanent revolution, new democracy, and the joint dictatorship of the peasantry and the proletarian.
According the TWCS, the proletariat should rally behind a leader and institute a breakthrough military coup, institute a people's war, follow a focoist military strategy, etc. After this, the bourgeoisie and it's allies would be suppressed and a dictatorship of the pan-national and national petit-bourgeoisie with the support of the proletariat would be instituted. A state-capitalist economy with the absence of the bourgeoisie would be instituted. A cult of personality behind the leader would be propagated to get the support of the peasantry along with a form of progressive militarized society. The ruling party really has the power rather than the leader and liberal opposition parties would be suppressed in a form of managed democracy. Along with this, communal power would be propagated. The autonomy of these communes would be dependent on material conditions, but too much autonomy (such as arguing for "states rights" or "municipal rights" would be frowned upon) would not exist. There would be a right-wing populist party (economically left-wing) called "The Party of Order", a left-wing populist party called "The Party of Liberty", and a centrist party to stand between the two. A proletariat party would exist outside of this and act as a opposition group that would also help harass "liberal opposition" protesters, etc. Eventually, the TWCS state would lose it's progressive character. When this happens, when the proletariat make up a majority of the population, the proletariat are faced with 2 main options. Either the proletariat could make a revolution to overthrow the now reactionary state or the proletariat could hope to make a constitutional overhaul with massive proletariat support (violent protests, etc.). Here, think of Daniel DeLeon's SLP campaigns.