Hello. I am planning on putting in a tile backsplash in my kitchen, behind sink and stove, along the wall. Pretty standard, I suppose. Can I put the tile right onto the drywall, or do I need some kind of backer board to adhere it to?

Thank you.

Right on the drywall is fine for the splash. Make sure it is clean and use a good tile adhesive or acrylic modified thinset. Grouting will be important since kitchen grease can make a great job look terrible. Either seal the grout or use a 3 part expoxy grout, about $25 per quart.

I agree, no need for a backer board. Use mastic and a notched trial, I use a 1/4 for floors as for a wall I usually use the same thing but you can go smaller for smaller tile 1/8 or 3/16 will work

As for the grout the 3 part is a pain to mix up especially when you leave out one of the those parts lol. You can grout the hole back splash and then after it dries you can vacumm it all right back up. What I normally do is use regular grout and then seal it. The sealer I use runs around $30 but it can go way up from there.