Strollerderby

If you were having a conversation, I would say continue the conversation the same way you would if she gave the baby a bottle. As far as looking or not looking, you should look at her face while you are talking.

I as a dad always handed my little ones mom a receving blanket just so they didnt feel "on display" because it isnt a sexual thing, however it is an intamate moment for bonding between mother and child. so anytime i was in that situation i just went for stroler or car seat to get a blanket to drap over shoulder and baby. not only are you not feeling uncomfortable by looking or not looking you also seem very help full. that counts for alot new dads.

I agree with Manjari.  I mean, really, it can be startling at first, so I understand that.  Heck, I remember sitting next to a mother who started to breastfeed in CHURCH.  Try concentrating on the sermon, THEN!  But once the initial shock subsides, you realize that this is natural.  It's not even that it's beautiful or touching or some other extraordinary thing... it's just a woman's body doing one of the many wonderful things it was made to do.  

So, look.  Turning away suggests embarrassment or that she's doing something she's not "supposed" to do.  I mean, don't gawk, that's creepy.  But, honestly, if she had a problem with you seeing her breast, she'd cover up (or excuse herself).  So, take a second to regroup and just continue on with your conversation.

Don't look or not look. It's just a breast. Pretty much the same skill as not leering at clothed breasts.  

Continue the conversation. Even if you are standing. If you want, excuse yourself to get a chair so you will be more comfortable, but clearly, if she began breastfeeding in front of you, she's comfortable enough.

Sorry, I mean don't "look" or "not look".

Watch for body language. While she's getting set up and focussed on the baby, you can casually examine the room, check your messages, etc... Once they seem set, check for eye contact. If she's staring at her baby, she probably doesn't want conversation. If she's looking around or making eye contact with you and/or others, keep talking and making eye contact just as when she's not nursing. She may glance at the baby now and then but that doesn't mean the conversation is over.

i say continue the conversation.  if the mom felt uncomfortable about baring her breast she would have figured out a way to avoid doing that (going into another room, getting out a hooter hider, etc).  Though I will say I think it's kinda strange for the mom to bare her breast while talking to a guy - it can make people uncomfortable and while I breastfed anywhere/everywhere I didn't want to make others feel awkward.

Ask if you can have some. Just kidding. Just carry on "dude"...or if you really feel uncomfortable, offer to get her a glass of water. Nursing moms needs lots of water. If she already has water, try first suggestion.

It's OK to acknowledge what's she's doing. I'd say, "Oh, looks like she's hungry. Are you comfortable, or do you want some privacy?"

If she says no, just keep talking to her as if she were giving the kid a bottle. If she says yes, offer to help her find a corner or private room.

I found it annoying and a little insulting when people (even my husband) would try to get me to cover up while nursing.

I do the best I can to be discreet in public. I know it makes some people uncomfortable. However, around my best friends' husbands (my best friends are also nursing moms), we just let it all hang out and be comfortable.

In other mixed company I try to be discreet. However, once she could grab things, my baby would rip away anything I  tried to lay over my shoulder and shield her. She found it distracting, obviously, and it made it hard to re-latch her when she's come off. So, from my POV, encouraging a friend to cover up is a no-no. Let her be the judge. If she wants, she can always say, "Can you hand me that scarf?" or whatever.

Great question!

Don't worry so much. As long as you aren't staring at her and don't make a rude comment (looks like a great lunch), you are probably ok.  Finish your conversation.  If you aren't sure what to talk about, ask about the baby.

If you feel uncomfortable (and clearly you do), you could steer the conversation towards something in the mother's sight but which you would have to turn to look.  At a party, you could offer to get her something to drink.

I figure if you pull your boob out in public you dont mind men looking at it.  People automatically look at babies.  If they are hanging on the boob people will still look at them, even touch them.  So if you are shy about your boobs dont feed in public.  

I'd guess that if she hasn't excused herself, she's comfortable.  Just don't gawk.  (Said from a nursing mother, who notes her surroundings before "whipping it out"/accommodating a child who has just figured out how to pull my shirt up)  I have a sense about those who I can and can't nurse around, and am discreet (as I can be anyways) if there is any question in my mind about it.  

Often while breastfeeding in public here in Italy, some old guy (like my grandpa's age) will walk up to have a peek at the baby. I used to think 'uh-oh, he's going to be embarassed when he realizes that I'm breastfeeding' but these guys aren't.  He'll take a good look at the baby attached to my nipple, make some chit-chat and go on his way.  

    The first time that happened to me was at a family reunion in the living room of my grandparents farm house.  She was a cousin, three years my junior.  Everyone, even she, continued the conversation as if it were an every day event, although it was not.

    Both of my grandparents were there, but he passed away in 1967.  They were not let it all hangout kind of people.  I guess it seems strange to me that a question like this would even be addressed 40 years to late.

    I am a seven tyyear old male, by the way, who has conversed with many women who breast fed over the years, and many who werebrest feeding while we conversed.

   If the conversation is worth beginning, its worth carrying on in spite of 'minor' interruption.

first of all, banish the thought from your mind that a woman breastfeeding is "on display like that"

she isn't on display.

I've nursed in public many times. Most times, you really won't see breast. Maybe top, etc. And, I agree, continue the conversation. Most moms will give you the cue that breastfeeding is about to begin. If you aren't comfortable, I'm sure you can find ways of excusing yourself from the situation.

I remember when all of the families from my wife's prenatal yoga class were together for the first time and all of the Dads were talking to each other while looking at the sky while the little ones were getting their lunch. Obviously a ton of support for the breastfeeding, just no one wanting even the slightest hint of leering.

Like many others have said, just look the mom in the eyes and continue with the conversation if she seems comfortable.  If you're really too uncomfortable, you could politely say something like, "I'll let you focus on feeding the baby.  I'm going to go grab a drink.  Do you want anything?"  That would allow you to leave while also being polite.  

I don't understand why a few commenters are saying that certain places are inappropriate to breastfeed, like church.  Is it inappropriate to bottle feed in church as well?  I'm not trying to be snotty or anything, I'm just curious.  I'm fine with a baby being fed in church either way, but I don't know what the general perception is!

I'll join the chorus of "just get over it." If she's okay with it, you can be, too (not saying you "should", just that you can.) Otherwise...

If you're perfectly comfortable staying but are worried about her sensibilities, I really like Zoe's suggestion. I might even suggest, "Do you want me to give you some privacy?" to emphasise that you're not suggesting that she change what she's doing, rather you're offering to accomodate her.

If you're more worried about your own sensibilities, J's suggestion "I'll let you focus on the baby..." lets you exit with grace and without blaming her, even if she figures out that she "made" you feel uncomfortable.