War against another nation
Micronations can declare war on other micronations just like other countries. However recognized counties (called macronations by the micronation community) typically will not recognize it as a real war. As such they may arrest anyone who participants in the war if the war turns violent.
Prosecuting the war
Micronations usually fight war jokingly, since if the two micronations would actually fight with weapons, the actual recognized countries nearby might declare the micronations violent (although in some cases, such as during the Molossian-Mustachistani War, surrounding recognized countries instead remained neutral), and try to take over. Some also fight in non lethal ways such as paintball or airsoft this is to avoid begin arrested by macronations.
Ending the war
Micronations most commonly end wars with peace treaties, declaring peace between the two nations. However some do end in one side surrendering.