First, a quick word about mountains … plate tectonics. Mountains form where continental plates overlap and one plate is pushed down and another is pushed up [or] where magma punches through the plate (again usually along the crack between plates) and pushes up a volcano. When this happens in the ocean, only the very peaks are visible above the surface.
Second, look at some real islands:
Notice that the mountain ridge tends to run along the center with flatter plains along the coast. Note also that rivers, when they occur, tend to be short and run from the edge of the mountain to the coast. Note also the frequent occurrence of lakes at the foothills where the mountains transition to coastal plains.
For your map, I suggest that you first decide where the ridges run – perhaps along the center of the bottom and left land masses. If you want a continuous ridge, then place the mountains continuously along the ridge line and transition to hills where the ridge approaches the coast. If you prefer more distinct mountains, then pick several points furthest from the coast to be the peaks of the mountains with hilly terrain around the mountain and perhaps a flat plain between them.
I hope that helps.
[PS. Just a quick note that the ridge can run along one side of the island rather than down the center, creating a steep rocky coast on one side and broad plains sloping to the sea on the other.]