Pick a route, avoiding the steps and loose gravel as much as possible, pull the front wheel up over any significant obstacles, sometimes the hit is enough to stall you, or throw the front wheel up into a wheelie which veers off to one side, as said by others ease off where you know traction is limited.
Don't try to hard, go up in the easiest gear at 70% effort (if possible of course) leaving reserves for control and manaeuvering the bike.
If (when) you stand up it's important to keep your legs pedalling cicles rather then jumping on top of each power stroke and letting your weight do the work, this is a vital tactic to avoiding wheelspin. If you
have got front suspension, try and keep your upper body as still as you can, if your forks are bouncing up and down like mad then you're using your weight instead of pedalling circles.
Depending on how steep it is you may not be able to sit down and keep the front wheel down for any of it, having to stand all the way. This is really hard work so practice standing up and pedalling circles for a duration long enough to get you to the top of said hill, even if it's top gear on the flat to get your legs used to that riding position.
Full sus is often not great on the steepest of steeps, with your weight pushing backwards due to the hill, the rear compresses and the front raises (without lockout) effectively raising the bars making it nigh on impossible to keep the front down, I find they can bog down eating all your effort into the suspension instead of managing to go forwards at 3mph, give me a rigid for hill climbing any day.
edit - Don't forget to breathe, it's easy to find yourself holding your breath whilst concentrating, I did this for the first 10m of a climbing wall once, suffice to say i didn't make the remaining 10m!!!
Tyres - Full fat knobblies are the order of the day, worn or semi slicks, give up accept you're ride average will be faster despite the walk up the hill.