How to open this fluorescent light fixture?
On the fixtures like this I have repaired the bezel comes out. Pressing on the bezel down flex in then pull out , did that make sense ? 
There are normally 2 clips evenly spaced from the end, normally on the short side of the bezel or plastic lamp cover a light pressure to flex the plastic towards the fixture push like you are putting it on (not all need this but some won’t release with the removal of tension) then while still pressing pull out.  I hope I explained it better. These fixtures are very common most often in a 24” model but I have seen 48” ones. The lamp is normally a standard T8 or t12 bulb I would guess at A T8 and they do go bad. 

If you go to a big box store they will probably have one as these are common but today they may have an led lamp. Ask to look at it and to look at the bulb or what type of bulb you need to purchase.