Please don't stay away. There will be pleanty of people who'll "avoid" her without meaning to because they don't know what to do or say.
Go over to her house, look her in the eye, tell her you don't know what to do or say, but that you love her.
If you can be devoted:
Call her and tell her you're thinking about her 2-3 times a week.
Visit once a week to SEE how she's doing. Listen, and LOOK around. She's going to be completely overwhelmed and not know where to start. Something will have to fall through the cracks because there's no more back-up from daddy. Help tidy the front room, help start dinner, help her figure out a new budget, offer to take her to places that may be difficult, see that she's eating, see that she doesn't cacoon herself too long, see that her laundry is making it to the washer...you know, LOOK around and simply start in and aiding because we generally don't ask for what we need.
A very important thing is to NOT offer something you cannot be committed to 10000000000 percent in an inconvenient time...and longer out than 2-3 weeks. Often people offer things that they mean at the moment but are not committed to, so when the time does come that the person in need brings themselves to the phone and musters the courage to ask, the reception of this opportunity to serve is less than generous.
Be sure you honor where she is at any given moment.
Hugging, holding, sitting near by are good things.
Allow her to see your sadness about her situation and the loss of her husband. "I'm so sorry" is a good thing, a normal thing to say...followed by, "I don't know what to say" is appropriate. "How are you doing" is something people say a lot, but, really, what's answer supposed to be?
In a few weeks, allow her to be her normal self and share concerns and frustrations of your own life...just like you would have before--so don't over share or undershare...be normal so she can, too.
The key here is to plainly and committedly BE HER FRIEND. Come from your heart and it'll be difficult to stumble much.
OH, I almost forgot: Encourage her to take her time in clearing out hubby's items. Some may want to come take everything out to remove reminders thinking it will help heal and motive her to move on...this can be DANGEROUS and very upsetting!! Give her validation in her right to keep anything of his for as long as she wants. Removing things can be very, very emotional or move quite quickly with a rebound of emotion later...so it's best taken at her pace. Mothers, brothers, sisters, etc...may want tokens from her Hubby, she may need some help with that so you could go visit and after a long visit you can gently ask her if there's something she's planning to share with his Mom and reaffirm that she has all the time in the world to do so but that it'd be nice...and then quickly redirect conversation unless she's into the subject with interest.