I'd like to build a chef holding a flat tray to put cookies on. Is there a way to get a hand to clip to a large tile or something like that?
You could use this Serving Tray
Surprised this hasn’t been mentioned in any of the other answers, but a Minifig hand is perfectly in system: it fits anything bar sized inside the hand, but the top of the hand is also the size of a regular stud, so it can and will connect to anything with an anti-stud hole, such as the bottom side of a 2x2 or 2x3 plate. Place the plate on the hand and you have the top studs to safely place bakery items onto without them moving around. This is used in many sets.
In addition to specific minfigure untensils for tablets and trays as shown in the other answers, you can as well just use an actual tile (or, for fixing the cookie, maybe a 2x2 jumper tile). Judging from existing sets, a minifigure holding a tile in their hand is a perfectly legal building technique. Of course if it's a tray rather than, say a smart phone, you probably want to rotate the hand sideways so that the tile lays flat with regards to ground level.
I have used a 1x1 stud plate (6141) and a disk or plate. These are found in almost every large-ish Star Wars set. I have also used a kitchen equipment piece (34172) that has a stud on the bottom. These should be found in some polybags or LEGO HOUSE sets. To hold it vertically, use a 25893 3.2 Shaft w. Knob stud. It has a small shaft for your cook minifig to hold as if he were holding an empty tray to go get loaded or cleaned. These can be found in many LEGO MINECRAFT sets.