hello biyclegirl. it can be done. find the studs in your walls . take exact measurements as to how far apart they are and mark them on your shelf. use an auger bit (a long drill bit) 1/2" in diameter to drill into the studs ( less than 2x1/2 " deep) and the shelf about 1/3 into the width of the shelf. it's very important to keep the bit at 90 degrees of both surfaces . take what is called an all thread ( pin or bolt?) it has a self tapping screw on one end and a bolt end on the other. screw the tapping end into the shelf and with a rubber hammer to tap the bolt end into the wall. again, it's important to keep drilled holes at 90 degrees. if you need step by step instructions let me know.

Wow jeff, thanks for these great instructions! I actually understand most of this! I have a want to be carpenter friend that's going to help me with this, so I'll be in good hands...hopefully! Stay tuned, I might be back for more instructions!!

Seriously, thanks. I was worried since my house isn't a new build, I was going to have to use brackets.

Don't want to be a downer but Jeffs idea will not work.What he is calling all thread are actually hanger bolts.How are you going to drive a "bolt end "made for a nut into a stud and make it work.

no downer here precisioncarpentry.... you thread the screw end into the shelf , the bolt end is tapped into place using a rubber hammer on the shelf. at 2 1/2" into a stud it's not coming out. it ain't pretty, but it works. anyway bicyclegril found the made for this job hardware. i might order some myself.

Just use pieces of 3/8" grade 8 all-thread and Hilti bolt-setting epoxy. But make sure you get it right the first try, because there will be no second chance.
Casey