That "Need to go" feeling...

For me, it just took experience. If you're newer to it, that feeling is there because the only time you're normally relaxing and stretching your anal muscles is when you're having a bowel movement. Using a plug regularly and playing with toys and fingers got me used to opening up in a non-bathroom context. Also, if you make sure your diet is balanced so you have regular healthy bowel movements, and (as an optional step) use an anal douche or enema before any play you can be assured you don't actually have anything in there waiting to come out.

Practice. You've just got to get your body used to things being in the rectum that don't need to be pushed out.

A midsized butt plug may help with this - put it in for 1/2-1hr periods.

There was a thread about this before. You might want to take a look at that one for more perspective on this topic: link

I agree with other people's advice, just play around with putting fingers/toys in there and eventually you'll get used to it. Although I will say I still sometimes get that feeling if I'm not turned on during anal, so be sure you're into it before you do it!