I think the genuine answer is 'with difficulty' for a lot of LPs, particularly those with very young DC.
I was a single parent for the first 6 years of my DC's life. I had twins. I went back to work when they were 6 weeks old and was back full time by the time they were 6 months old. I left my then DP when they were 4 months old because I thought life wasn't challenging enough as it was 
(long story there but not relevant to this thread). XDP maintained an interest for about a year, but then pretty much disappeared apart from the odd Xmas or birthday and never paid any maintenance. No GPs on either side so I really was on my own apart from some very dear friends, one of whom I would lay down my life for she has been so amazing.
You get through it because you have to. You wouldn't be human if you didn't get exasperated hearing couples arguing over who does what when you're thinking 'but I have to do it all'', or when you hear someone moaning that their lie in has been cut short when you're thinking 'my last lie in was some time 2.5 years ago.' If you're going to survive it with any degree of enjoyment, you learn to be ruthlessly organised to minimise times spent on essential chores and maximise 'me' time. I batch cooked and cleaned up as I went along so that I never had to face weekends cleaning for example.
On a practical level, once the DC started sleeping through properly and I wasn't so thoroughly exhausted all the time, I found I could cope quite comfortably. I'm sure you will too. For me, the difficulty came with money and lack of fulfillment.
As a single parent with no maintenance coming in but a full time job requiring paid-for professional childcare, I found myself worse off than someone on benefits for the first 4 years of my children's lives. I often went hungry and had cardboard in my shoes because I couldn't afford to replace them. I felt I all I was doing was exchanging one set of responsibilities (work) for another (children) with nothing for me in between, and with no money there was no opportunity for me to go out to blow off steam or to spend money on retraining into something better trained. By the time my DTs were 4 and started school I had used up nearly all my resilience getting to that point.
However, once they started school and my childcare costs plummeted, all of a sudden there was a little money left over for socialising and retraining. Fast forward several years and I now have a life totally unrecognisable to those days sat in my own living room in fingerless gloves drinking a cup of tea from a reused tea bag. I have a great, challenging new career with a decent pay, promotion and pension package. I can't afford to be reckless with money but I don't have to think about whether I can afford a pair of shoes any more and my heart no longer sinks when I get a letter home about a school trip requiring £20 or whatever.
Once the money situation improved and I felt I could be me instead of only mother or employee, I actually began to really enjoy being a lone parent. Far from finding it difficult, I found it quite liberating. So much so that when i met my now DP I seriously considered not moving in with him because I liked being a single parent so much.
For me, I think the experience of being a single parent varies hugely depending on money and support. My advice to you would be to cultivate your friendships, particularly with other single mums. My single-mum friends got me through my darkest times, commiserating with me on bad days, cooking me a dinner if money was really tight (even though they often had none either), being on the end of the phone when the DTs left me at my wits end or my bank statement was still in the red after payday. And we'd share a bottle of wine and laugh til we cried when none of us could afford to go out anywhere but needed to let our hair down. Being single mothers too, they were happy to sleep on sofas etc and the DC would share beds in a way that doesn't really happen with couples.
Hang on in there. You will cope, and as you get more used to it you may find you actually love it. 
