Lovingtyrells
The tools for helping put baby down to sleep are:
Plentiful calories
Hunger, either discrete immediately before a feed is due or low level whereby total calorie intake over 24h is less than baby wants, is always going to give you a clingy baby who wants to be held. It is not that all babies who like to be held are hungry, but you wont get an easy-to-put-down baby who is hungry.
Dummy
The natural, newnorn sucking reflexes is soothing and calming for a baby. It is why most networks will fall asleep when feeding. The dummy is the simplest and easiest no-crying sleep tool
Swaddle
In the newborn phase, in particular the first few weeks, babies are soothed by recreating womb-like conditions. In the womb baby was cramped tightly into a small space and fully enclosed on all sides. This is the feeling that the swaddle taps into - tight, enclosed, secure.
Keep the swaddle right around arms and shoulders, loose around legs and hips. A baby fighting against a swaddle probably needs one more, because once enclosed (and with a dummy) baby can start calming down and soothing.
Plentiful Sleep
Good sleep promotes better sleep. Poor sleep results in even worse quality sleep and so you get into an over tired cycle.
In this early newborn stage, baby should mostly sleep all the time. Over 24 hours a day. Many parents are surprised how much sleep a newborn needs and don't realise that my 'entertaining' their newborn they are creating an over tired cycle. At 4-6 weeks old baby should literally just wake, feed, have maybe 10-20 minutes floor time and then straight back to sleep. Throughout the day baby should be awake no more than 1h at a time, in the range of 30-45m awake time is ideal, including a feed. During the night, just feed and straight back to getting to sleep. The only time baby might be awake for longer is the evening clusterfeeding marathon that breastfeeders often do.
If baby is over tired, it's not the end of the world. But does require you to notice tgat that she is and put in significantly more effort and focus to get baby more sleep in order to get out of the downwards spiral with sleep.
Movement
This is an added extra-help way to get baby sleeping. Easy hands-off ways to allow for movement to sleep is the bouncy chair. I use the bouncer for all daytime naps. If baby goes to slerp easily in the cot, great. If not, try a bouncer.
Another obvious way to allow for movement to sooth to sleep is rocking baby in your arms. The problem with this is that baby doesn't go to sleep where he stays asleep (ie goes to sleep in your arms, then stays asleep in the cot). It's really not a problem to rock a tiny newborn like yours to sleep. But as you head towards 4 months, an approach that allows baby to go to sleep where they stay asleep (with movement if needed) is most helpful.
Your Presence
Another factor of recreating womb-like conditions for comfort. Baby is used to feeling you, hearing you, touching you, seeing you, always being with you. Your physical presence is in itself a comfort.
So touch is important. I got baby used to feeling my hands on her chest when she went to sleep, so she knew I was there. I also knew the benefit of my head hear baby's as she goes to sleep - to hear me breathing in her ear, feel my breath on her cheek, smell my smell close to her.
Some other parents choose to cosleep or cuddle to sleep in order to give baby this reassurance. That's fine, it's not the only way to ensure baby is comforted by your presence though. Committing to giving baby your time and focused attention when going to sleep helps, rather than assuming it's a passive thing whereby you should be putting baby down and leaving.