Anal giving means that your partner is willing to give anal sex to you, either with their penis or through the use of a strap on. This gives you the chance to experience what it is like to be penetrated, which can leave you feeling fantastic and also fulfill a desire that many people have but don't act out. You can start with some light anal play first before moving on to full penetration, as the control should be with you.
One of the most important things to remember about anal play and anal sex is that there is no rush. Some mistakenly think it is better to get straight in there so that they can get the pain over with, but it is better (and safer) to take your time. Working your way up will mean that, not only are you more relaxed, which will allow your partner better access, but you are much more likely to enjoy it and want to try it again. Using plenty of lubrication can also help, as your partner can slip inside you a little easier.
If you are looking to try anal play, remember to clean thoroughly. Simply standing in the shower and allowing the water to pass over you isn't enough - you will need to actively get the nasty surprises out of there. Using warm water and soap, lather yourself up all over to get yourself nice and relaxed before you go to your ass. Very carefully clean the general area before focusing on your asshole. Slip a wet finger slowly in there, gently rubbing to remove any of the stuff that has accumulated there. Give yourself a thorough clean and you are good to go.
When it comes down to it, tell your partner what you want. If you'd like some rimming before your take their surprise, let them know so that you can be fully relaxed and enjoying yourself before it happens. If you need to take a break throughout the proceedings, tell them. It will ensure you both have a great time while also respecting your boundaries.