I'd highly recommend an "MOT" or a check by a women's health physio before you get going. With my first, I didn't know better... I just went out for a 5km run at 6 weeks post partum and thought that was ok... but being a bit better educated now, I will certainly be checking that everything is well healed and I'm not at risk of prolapse/don't have abdominal separation etc - or if I am, focus on fixing those first.
Once baby was 6 months old, I went out with her in the running buggy, which is wonderfully liberating! (There is a fab facebook group called the Original Buggy Runners/Active with Kids for lots of help and support from like minded families if you're interested in running.) They don't recommend buggy running before baby is 6 months though - or in a normal pushchair without suspension/with small wheels etc.
Prior to that, I had a mile lap from my parent's house, which I would go off on... that way, every 10 minutes, I could be stopped to feed the baby etc... and even 2/3 laps was great for building back up.
Home fitness videos on youtube are fab - there are SO many HIIT classes etc on youtube - and most of them only take 15-20 minutes... I would recommend them as they don't need you to leave baby.
The other option is to do it before your partner goes to work - or after he gets home.
In the early days, it's all about being kind to yourself - yes, you're keen to get fit again, but remember, it takes 9 months to grow a baby, it takes the same for your body to heal... and as they get older, your independence grows immensely, which makes it a lot easier :-)