When I first moved into my house, the two fireplaces had that ugly mesh fireplace screen, rusted and dirty. I demoed the one fireplace completely but the other stayed so I decided to make a really simple glass screen. This is probably the easiest DIY you can find.
I made a quick stop to a local glass shop for a sheet of 3/8″ tempered glass with polished edges. This was a little while ago but I believe it was around $40. I then stopped by the metal shop and picked up some 2″ x 2″ aluminum L for around $10. I then glued them together with construction adhesive and clamped them to dry for a day. I added little felt pads on the bottom for easy moving around to clean.
We don’t really use this fireplace outside of lighting candles on occasion but in case we did I left a 2″ gap around the outside edge to allow for heat to escape, but you can also bring the glass out from the opening to allow for additional heat to escape.