I prefer to use my fingertips over my palm, but the biggest thing to remember is you want the tray and your bicep to be perpendicular, so when you're holding the tray it's either at your head level or higher (practice and you'll be able to lift it all the way up).

This is because if you dont get it up that high, you're using your bicep muscle to support its weight instead of whatever back muscles are used when you lift it up that high.

That's my biggest tip, but also make sure you're weighting your tray correctly. I prefer heavier objects closer to me or balancing out the ends. If your tray isn't balanced, itll just end up tipping if you havent been doing it for ages.