Here's a basic overview of mountain creation on Earth.
Mountains are created in three major ways:
Volcanism, Faulting, and Folding. All three of which are associated with Plate Tectonics and mostly happen at plate boundaries with subduction zones.
Most mountain ranges on continents are caused by folding. Island chains are usually caused by volcanism. Faulting generally occurs where there's already folding.
For an example of folding take the Rocky Mountains in western North America. This mountain range was created because the Pacific plate is spreading in the middle and is forcing the sea floor to subduct under the western edge of the North American continent. This force causes the continent to fold up as well as some volcanism and faulting. So when you get coastal mountain ranges it's generally caused by a sea floor plate spreading apart and forcing up against a continent or two.
So in your map you have a problem with some mountain ranges being shadowed by other mountain ranges. (Meaning that it would be impossible for plate spreading to cause the mountain ranges hidden behind other mountain ranges.
Another cause for mountains is when two continents collide as is the case with the Himalayas. The Indian subcontinent has basically crashed into the Asian continent causing a huge pileup along the northern edge of the Indian subcontinent and the southern edge of the Asian continent. This is the way to get the largest and most severe mountains on a planet.
The Appalachian mountain range on the North American continent was caused by very old plate collision as well. It's just been so long since it happened that they've all worn down quite a bit.
Getting mountain ranges in the middle of a continent can be achieved through a "hot spot" which is an upwelling of magma under a continent that can cause volcanism. They tend to be much smaller and do not run in long lines.
This is a very simplified version of the process and you should check out Plate Tectonics on Wikipedia for a more detailed explanation.