why not RTM? (omg)
read the manual,
all this is covered there. how to CONNECT.
there is no phone support, apple or android. only xp to w10.
on newer printer, far newer, the phone can be linked to HP smart print servers and to your home system printers.
here is HP site page showing how to do that,
first pick a printer that does that.
using the smart app
there are many ways to set that up, but direct cell to printer.
no. (yes new products can do direct cell print)
that is called wireless direct print , features, as see here.
you said you have phone (cell apple or android?_)
then said have a laptop.
my cell , is android and I use local wifi , to save 3g charges
my laptop has internet connections 2 ways, wired, and wireless
does yours have wireless. seems not.? but.... do you?
you said no router, but if you go to any ISP today
and he installs internet service, there are 2 hidden router now
inside the old name modem,
the modern cheaper modem has that, hidden is side.
has 3 things in the black box.
so what do you have there that we cant see, devices to the ISP
with names and model numbers.
knowing that tells the helper what is possible , (all things)
my guess is you want to print, using the CELL.
if you dont have eprint mail the docs or photos to the laptop
then, print from Laptop
to printer using a USB cable, (USB is 10x more easy to make work)
your printer can connect up 3 ways.
Printer USB to PC. direct wired printing. ( always a choice, direct)
Ethernet to router. wired. (all things connected to this router can print.
wireless to router. printer to router joined, and print from any thing at home connected to said router.
if it must be wireless, (you must have that?)
then buy a router. and use that, and is safer behind any router firewall vastly saver too boot.