1. You may take a national flight to Bluefields, managed by La Costeña. The cost of flight is 126 $ (and airport taxes, of course). From Bluefields you proceed to Orinoco with panga (a big outboard motor -boat). The fee for the boath ways is about $ 24 or 570 cordobas. The boat trip takes about 2 hours and you should be prepared for the rain in rainy season (May-November) and sometimes strong winds and sharp waves of lagoon. Most of the times trip in boat is relaxing and easy going, though.
3. You can take interurban bus (bus station is by Ivan Montenegro -market place in Managua) and go to Rama first and then to Pearl Lagoon. This option takes whole day or whole night, depending your time of departure. The most exotic and very interesting bus trip through Nicaragua, but have to admit; it is not the easiest one.