How does heat pass through glass? So infra-red and ultra-violet waves from the sun heat up the glass by conduction then it then radiates this heat to heat up a room or a car? Is that right? 
How would one calculate how much heat a type of glass keeps out??
Also how does glass coatings like tinting 'reflect' heat?
 A: 
How does heat pass through glass?

It is not heat that passes through the glass,but electromagnetic radiation in the infrared range, in the same way as the visible light passes. Glass is transparent to visible light and to most of the spectrum before and after visible light frequencies , depending on the optical properties of the specific glass.

So infra-red and ultra-violet waves from the sun heat up the glass by conduction then it then radiates this heat to heat up a room or a car? Is that right?

No. You are thinking of the metal roof of the car that either reflects or mostly absorbs  all electromagnetic energy impinging on it,  and transforms the energy to heat that radiates inside the car according to black body radiation. Glass lets a large part of the electromagnetic radiation go through unscathed, which radiation entering the room will heat up the air etc by absorption.

How would one calculate how much heat a type of glass keeps out??

People have measured  and tabulates into charts the  optical properties of glasses. One uses the absorption coefficients to see how much energy goes through unscathed.

Also how does glass coatings like tinting 'reflect' heat?

It reflects the infrared radiation part of the electromagnetic spectrum by increasing  the glass' reflection coefficient for infrared radiation. It changes the refractive index of the material for infrared electromagnetic radiation.
A: 1] Air inside forms a free convective cell, with air flowing over the window. 
2] Heat from the air transfers to the glass, by convection. 
3] Heat transfers through the glass by conduction 
4] Heat transfers from the glass to the outside air via convection. 
If the temperature differences are small and there are no winds or drafts, transfer of heat to/from air/glass will be by conduction. 
Heat transfer by radiation will be trivial.
