>'if this isn't for you then you can go home'
Instead of practical motivators like weekend holidays and such, in more philosophical sense some of the better arguments in my opinion:
1. "So you don't feel like doing this and you want to go home. Consider this. If one day the shit gets real, are you sure there will be still home for you to return to afterwards?"
Many countries have Ministries of Defense and call their armed forces "defense forces". That sometimes makes me uncomfortable because the (not unintended) likeness to the Orwellian ministry naming scheme of 1984. However, compared to some countries, with some other countries a better case can be made that their military really exist for a defense of a political system against a potential immediate existential threat.
For example, South Korea still has conscription. European countries started moving to volunteer forces en masse only after the Cold War was over. Consider the political climate Sweden is in and why they suddenly think they need an army.
Of course, this is going to be as effective as credible the threat is and (more importantly) how willing the populace is to trust the their countries' political institutions. For example, looking at the map, Switzerland does not face any immediate military threats from its neighbors, but I understand that their conscript force is reasonably popular and motivated. According to Wikipedia numbers quite many people simply do not serve for some reason or another.
2. "If this isn't for you, then you are free to fill in the forms for declaring yourself conscientious objector and you will shipped to the non-armed civilian service to serve rest of you term ASAP."
This one hasn't been relevant in all conscript-based systems in all time and places, but in modern times it is. If the strategy does not call for absolutely every person capable of holding a rifle to do so, this is an option.
Additionally, if failing the service is considered shameful enough, the military may very well be willing to simply kick the unmotivated out.
In general, I believe it's more or less established that people are less likely to volunteer to do boring things, but if participation is mandatory and you need to do make a decision to get out, most people are going to do the compulsory thing. Of course, many people are quite averse to war because it's quite possible that you may really die, so usually the armies of the world make the "getting out" option penalized somehow. In the ideal world I'd actually like to see the "opt-out" version without any further penalties tried sometimes somewhere.
3. Additional forms of persuasion known to exist in various countries at various points of time are different forms of legal consequences, ranging from extra tax to jail to prison to death penalty.