Of course, you could avoid modeling the grating altogether by manually assign grating loads to beams using Assign > frame loads based on tributary area, but it can save time modeling the grating as areas and assigning grating loads using area load units (psf) and letting the program distribute lineal loads to beams automatically
If you decide to model the grating, you typically have vendor data on the selfweight, so you don't want ETABS to calculate selfweight.. and you also often don't want grating selfweight and live loads to be transferred to bracing underneath that you may have modeled. SAP makes this kind of modeling easier, but ETABS should also be able to do the trick using the property modifiers. First, you'll want to define a steel type material for your grating with zero weight and mass (you'll assign selfweight from vendor data and live loads later). Then define a slab membrane type using this newly defined zero weight grating material. After drawing the "grating slab" areas, select these areas and assign automeshing to de-activate the area automesh option (turn it off) for the grating in order to avoid transfer loads to any bracing underneath.
Also, you probably want to use area section property modifiers to minimize in-plane stiffness 11 and 22 directions of your grating (.001 or whatever) so that it doesn't affect your lateral resisting system. The property modifier can be a lifesaver in situations like these.
Then go back and assign your area self weight and live loads using area units (psf, etc) to your grating areas. ETABS should distribute these area load as distributed lineal loads to beams, but you control this load distribution by the way you draw the grating slabs with the auto-mesh turned off. This enables you to span grating across beams and bracing without having to distribute load unless you want to.