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The first thing is to clean the air filter and the exhaust duct really well, because lint and debris build up in there and burn when it heats up. I had a dryer that sat in the closet for a few months, and when I turned it on there was actual smoke coming out - it was packed with dust inside the drum itself. I ran a damp cloth through there, cleaned everything out, and the smell went away.
Did you leave the dryer stored for a long time without using it? Then that's it! That smell is dust, fabric residue, and moisture that built up inside over months of sitting around. When the heat suddenly kicks on, all of that burns and releases that pretty scary-smelling odor! It's completely normal and goes away quick - usually after one or two cycles the smell is completely gone. If it keeps smelling really strong or has a burnt taste even after that, then yeah it's worth checking if the heating element isn't having issues, but most of the time it's just buildup that needs clearing out!
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