Summarize:

When you're out for a walk, it's a chance to spend a moment alone together. It's also a natural time to have a meaningful or sweet discussion with her and, since you'll already be walking side by side, it's a perfect scenario for you to put your arm around her. Avoid discussing anything heavy or negative. Walk slowly and keep your body language relaxed. Suggest taking a stroll with her at a nearby park on a pretty afternoon. Another good excuse for a walk is to go window shopping or run an errand. Wherever you happen to be hanging out or whatever you might be doing, always try to sit or stand close to her when it makes sense to do so. Obviously, don't follow her into the bathroom or anything like that, but in general, staying by her side creates a "couple" atmosphere and provides ample opportunities to get your arm around her. If she seems uncomfortable with your nearness or makes excuses to get away, give it a rest. You want her to feel liked, not stalked. If she looks cold or if you happen to be out together on a windy or overcast day, be a gentleman and offer her your jacket. Not only will she think you're romantic, but putting your jacket over her shoulders provides an excellent opportunity to sneak your arm around her. Place the jacket sweetly around her shoulders, and then let your arm remain naturally around them. Smile at her and give her shoulder a little squeeze after you're got your arm around her. She'll most likely look up at you when you do this, and you two will share a real moment of closeness. If all else fails, give this classic a try! Yawn a bit and naturally lift your arms up in a stretch, being as casual as you can. When you bring your arms down, put one of them around her shoulders. If this feels a little obvious, you can always overact the move in a very obvious, cheesy way. This will probably make her laugh, and you should too! Sharing a laugh will break the ice and create a sense of comfort and ease between the two of you, and you'll have your arm snugly around her.
Go for a walk together. Be near her. Offer her your jacket. Use the classic stretch and yawn move.