Ah, sorry, I see your ds isn't actually 3 yet. I've no idea whether what we did would have worked 6 months earlier, or whether it needed that little extra level of understanding that he'd developed in that time... Hope you find a solution that works for your little guy!
What finally helped us (also at age 3) was what I referred to as "controlled-NOT-crying".
Basically I told him that if he stayed laying down and kept quiet when he was put into his bed I'd always be back in 5 minutes to check on him.
The deal was that each time I checked on him, if he was still awake and was "being good" I would come back again 5 minutes later. Thankfully he didn't know that sometimes it was a slightly stretched "5 minutes"
He was told (and he definitely understood, at that age) that if he started getting up and screaming for me, I'd completely ignore him until he'd been back in bed and quiet for a full 5 minutes...
Sounds pretty cruel, I know, but we were all at the end of our tether with sleep deprivation. This solution worked really well in that he had a real incentive to keep calm. To begin with I had to go back to him many, many hundreds of times before he'd be asleep and then do the same all over again for his frequent night wakings, but gradually he got more used to falling asleep without me beside him and so over a relatively short time he was asleep much earlier in the evenings and the night wakings reduced too
DS3 will be 3 in February and we are having major problems getting him to sleep on his own (ie he won't).
He was a proper Velcro baby from the word go and wouldn't let me put him down until he was 18 months (hyperventilating etc) and is just so completely unlike his two older brothers who we treated exactly the same - co-sleeping until 1 and 18 months respectively and then painless transfer to cot.
We had some success last January and actually got him sleeping most of the night in his own bed, but his waking, climbing out and clambering into my bed got earlier and earlier until we were back to him just coming straight to bed with me - not helped by me being pregnant with DC4 and desperate for sleep at any price.
I know I should have been firmer, but I wasn't, and now when he wakes in his own bed after an hour or two he just climbs out and wanders round the landing crying for me and waking his brothers up...
DC4 is due in January and I will be EBF and co-sleeping and don't feel comfortable adding a wriggly three-year who doesn't just want me next to him, but my arms around him into the mix.
This morning I'm a mess from getting in and out of bed three of four times (I can't actually remember) and spending the last three hours asleep in a single bunk with my arm up by my ear. My back is wrecked
Good job he's cute . But I am desperate for any tricks, tips or advice (or even a totally failsafe solution )
I should add that DH is very supportive and more than happy to get stuck into sleep training at the weekends, but works the most ridiculous hours during the week (bed at 1.30-2am and up at 8 for school run, then straight to work), so this is really on my shoulders (ouch!) during the week...