Hi Whitey, welcome back to cycling.
If you're riding with a club, get someone to show you how to stand. Try it coasting first, get used to moving your weight around, and then try pedalling. It's much easier to learn trundling along a bike path with someone beside you than by reading descriptions on a written forum.
Oh, and it's for the short gruelling climbs. Standing up is a great way to give yourself a little kick of power in order to maintain your momentum in a steep pinch or for a short climb. It's not the best way to tackle a long hill. Staying seated and keeping the cadence (leg speed) up will get you up the hills much better in the long run.
BUT, being able to get in and out of your saddle without wobbling all over the road is a very necessary skill to have. So keep practising!
IF, you need some "lady" specific coaching (never did get why we have a separate thread myself - as this question applies to any newcomer to cycling) then there are some women's only coaching groups and rides. Scroll down through this Section or try the BV forum search function.