You need to see it as short term pain for long term gain. That really is what it amounts to.
You can decide not to tackle it because you are exhausted.....but then you will be exhausted for an awful lot longer.
You need a plan. Having a very specific way forward and knowing how long you need to do it helps. You need to stick to the plan, even if it means In the short term you get less sleep.
There are numerous approaches and you could spend time researching and choosing. There will probably be a bit of crying, but if you time it, you will realise that what might feel that hours of crying is actually minutes....knowing that helps you deal with it.
Firstly ensure child is eating enough in the day...so having enough milk for their age and also enough solids. This will give you the confidence that they are not waking through genuine hunger.
Ensure they are in a daytime routine, because the better the sleep in the day, the better at night. At this age, I would think it means a short morning sleep around 9.30/10 of about 45 mins and a longer after lunch one of about 2 hours. Best to go down by 12.15 and not to be sleeping beyond 2.30 to ensure that nap doesn't prevent them being sleepy at bedtime.
Consistent bedtime routine, if winding down activity, bath, feed and bed by 7/7.30.
If necessary in short term, a feed at 10 ish. If not, get to bed yourself by 9.
Then responding to night crying.....yes to going into crying baby (although wait a few mins when they start, as sometimes they will go back off....need to learn to self settle, and can't do that if an adult appears within seconds of waking and crying) Don't put the light on, don't lift out of cot, gentle strokes for a few mins and then leaving. Return after 5 mins, repeat, repeat, gradually extend. Be brave and don't give in although you will want to. Keep going with it.
In the morning, ideally let them wake and have a little time just lying in the cot before going in.....it's all about them developing a sense that they can be in bed happily alone.
And I'd do it sooner rather than later, as it will get harder to sort.
One friend hired a night nanny to sort it out over about 2 weeks. Cost her about a grand, but she says it was the best money she's ever spent. Realise it's not an option for many and most can crack it themselves.
Good luck. Although it's not something to look forward to and will be grim, you can have confidence it will work if you keep going.