Without private transportation, getting to Isla del Tigre is a bit tricky. If traveling south from Tegucigalpa towards Choluteca by bus, you need to get off just before San Lorenzo for the turnoff to Coyolito. From here, you can catch frequent minibuses (L20) or hire a taxi (L200) for the 1-hour ride. If driving, you can park your car in any of the lots near the seafood shacks in Coyolito (L40 overnight, though you can bargain for longer stays).
To get to Amapala from Coyolito, you need to hire a boatman. Throughout the day, they leave from the pier frequently, and you can pay the per-passenger rate of L20. If you have a group or arrive in the late afternoon when no one else is making the trip, you can pay for a full boat (L140).
With no banks on Isla del Tigre and little money coming in, there is always a shortage of small bills. Get change in Coyolito or elsewhere on the mainland, or you might be out of luck. If you are in a bind, try exchanging money at El Faro de Victoria.