Since you appear to be looking for ideas, quick an easy or maybe more detailed, I'll give these links. You'll see that there are not rules, you can use many different things.
Nest boxes
http://www.backyardchickens.com/t/41108/show-us-your-nest-boxes-ingenous-design-post-it-here/220
Nest Boxes
http://www.backyardchickens.com/t/4...-your-creative-nesting-boxes/80#post_12395882
What materials do you put in the nest boxes?
People use wood shavings, wood chips, straw, hay, shredded paper, Spanish moss, certain feed bags, carpet, or rags to name a few. I cut tall grass form areas I don't mow or weed eat and dry it. Try something. If you don't like it, try something else.
what can I use in the meantime, until I get the rollaway nest boxes installed?
Again. look at the links.
Where in the coop, should I place them?
Where it is convenient to you. You will wind up caring about that a lot more than the chickens will. The way I determine elevation is to determine where the coop floor is, including bedding. Then position the nests. Some people like the nests on the coop floor. Some like them high enough that they don't have to bend over to gather eggs, say you have a bad back. That distance from the floor might be different if you have a walk-in coop versus an elevated one that you gather eggs from outside. Then I position the roosts higher than the nests. Chickens tend to sleep at the highest point available. If the nests are higher than the roosts they tend to sleep and poop in the nests.
Horizontally you do not want them pooping in the nests from the roosts. If the nests are covered the top may be a droppings board. If they are not covered be more careful about them pooping from the roosts.
You'll need to position them where you have good access. I don't know what your coop looks like so I can't offer much there. When the chickens fly down from the roost they need a clear landing area. Try to position the nests so they don't bang into them on the way down.
Do hens only lay in the morning or all through the day?
Most eggs are laid in the morning but they can lay all day.
Do they know not to go in there and soil the boxes, or should I train them, how?
No, they do not know to not go into the nests to poop. A broody hen knows to not soil her nest. A laying hen typically doesn't either while she is laying. But when they are not laying they don't care. I don't know any way to train then either. But I give mine a lot of room outside and I have the weather that they can be outside all day so they are not hanging in the coop all day. It's just generally not a problem for me.
When they are sorting out the pecking order or a cockerel is harassing pullets some can use the nests as a hiding place. Again, I have a lot of room outside so they can get away out there if they need it, but with a small coop and run you may have issues with them hiding in the nests. My roosts are high enough off of the coop floor so mine go up there when they feel threatened instead of hiding in the nests. Some people with small coops and runs can have an issue with them hiding in the nests.
Anything else you recommend for a city girl with a country loving heart?
Mainly, be flexible. Try something. If it doesn't work, try something else. Very few things work perfectly the way we originally plan them. Don't be afraid to change if you need to. And think if your comfort and convenience. You are important. If you arrange it where you enjoy taking care of them instead of hating it the chickens will benefit.