Pop onto whoever you wanna send a gift to's player profile / den, tap on "send message" and then there ought to be buttons that say "start trade" or "attach items". If you want them to give you something in return, use "start trade" to avoid getting scammed.
If you are just trying to be nice or give someone a surprise, you can use the attach item button and they will be able to claim it without you needing to do anything else.