The two biggest things that help a baby sleep in the first 3 months are:
And the two bit of extra help if the first two don't work are:
(all the S's - swaddle, suck, sway, shush)
So start off with wrapping baby in a swaddle, this recreates the tight enclosed feeling of being in the womb. Also like being in the womb, it reduces stimulation so also keep loud noises or brightness to a minimum.
Sucking next - this is a natural reflex that helps a newborn feel soothed and calm. So either feed baby to sleep, or if you prefer baby to sleep independently then feed baby until sucking stops, then as you lift baby to wind them on your shoulder, give a dummy so that baby can carry on sucking.
I'd suggest that after you have fed baby, wrap in a swaddle sheet and pop in a dummy , and lift baby to your shoulder to wind whilst upright. Keep rubbing back until a burp comes. Then return baby to cradle hold (in swaddle) and reoffer milk (second breast or what's left of bottle) and feed while in the swaddle. Once baby has finished sucking the milk, replace the sucking with a dummy and again lift baby to your shoulder.
Stay still and just wait for baby to settle. But if needed sway/shush a bit (no need for this if baby is settling anyway). Then bend at the waist over the cot, so that baby stays on your shoulder and you bend with baby as you put baby down. Put on the cot mattress and leave your hand on babys chest for a while, as reassurance. Tap the outside of the dummy a little if baby grimaces or doesn't seem calm, this triggers the sucking reflex.