Not sure what the left or right side is? You can not cross on the caribe side from Nica to CR.
You can cross the main crossing on the CA1 Pan Am Hwy via ferry from Ometepe to San Jorge, and taxi hire to border CR, then buses every 30 minutes from border to Liberia, from border to Liberia is two hours.
The other option, if boats are running again, is to head from Ometepe to San Carlos, and explore the El Castillo areas, go back to San Carlos and get stamped out, then cross Rio San Juan at Los Chiles to CR Immigration. From here you can bus to La Fortuna or San Jose.
How many days do you have in CR? What are your interest?
Monteverde is very overrated, touristy, and far from anything, so getting there from Liberia is 4 hours on a shuttle, or all day on buses.
I would focus on Cano Negro, Tenerio/Rio Celeste and Rincon, before Monteverde.
You can also use Arenal area as a base, to explore Tenerio and Cano Negro.
Keep in mind the border with CR/Nica will be a nightmare of epic proportions, Easter Week, as 300,000-500,000 Nica migrant workers in CR head home for Easter, and then all head back to work. This is the biggest holiday of the year in Latin America...
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