TBH I just started shaving down there, and it can be done quite safely with a fresh razor and warm water in the bath, you will get a better shave if you take your time, and allow the water to do its work first.
Some people prefer to clip first, before they shave which makes life a bit easier.
A shallow bath with shaving gel and warm water will do a better job. Avoid using blunt razors, as they will cut you.
The trick is to be patient and not rush it.
Brand new razors work best, use warm water, and take your time!
Standing/sitting/laying down is entirely upto you, the more relaxed you are, the better the shave usually.
If you are planning on keeping that area forever devoid of hair, go out and buy a half decent electric razor, devoted solely to that area. I would not recommend you sharing it with your face. Battery operated single head shavers are fine, but I do not recommend rotary ones, as they can catch you if you have missed a spot.
Make sure the area is completely dry before you use it though, and tal
powder will help avoid any soreness aftewards.
After a few weeks I have got into a routine now, and it requires minimum effort to maintain. Its the first few attempts that sometimes catch people out...
Hope that helps...
I forgot to mention, I have only cut myself once and that was with an electric rotary razor (loL), never do that again !