Edit: I moved the tips to here once the thread became a sticky.

The two attached images show the basic use of the Trade, Repair and Identify windows. I did not show haggling.

I assume that you have clicked on a NPC to get the top left image shown in the first image. Also, some NPCs cannot repair or identify items, their repair / identify icons will be grayed out.

You can buy and sell at the same time by selecting the items to buy and sell and than pushing the scale icon for yourself and the merchant.

Offering the merchant items without clicking his scale icon is the same as giving him the items at no cost which can improve your standing with the merchant. The higher their opinion of you the lower the cost for items will be. Up to 100%, after that, cost stays the same.

You can haggle by entering less than the merchant wants after pressing his scale button.

Your pictures are not only useful, but also remind me how much I hate some of the character portraits in this game.

Thanks, this is . . ah . . ah . .. a test . . .=)
Any improvements or suggestions will be appreciated . .
Edit: I agree, the portraits are pretty bad . . .=P . . . that is the standard Survivor I believe

Its practically identical to fallout's trade system so I felt at home. It took me a while to notice the balance button though. I'd been happily playing the trade window like a mental arithmetic mini-game until I found it.

I'm just another community member like you. I have been helped many times by other members as well.
You're welcome, I posted this as a solution to your question.
I posted it here hoping it would be helpful to others as well. There is a link to this post there if you would like to mark it as a solution so others can more easily find this solution.
I was doing the same till I realized they were buttons . . .=)

Do traders ever offer anyway near the actual cost of the item? I'm still in the starting town, have the trader at 72 reputation, but he still vastly undervalues all of my items.

Early in the game, you are a stranger and merchants don't give much discount. As you gain more reputation and interact with the characters . . . the prices will come down. There are one or two quests that give you better prices from merchants when completed as well.
The number shown on each character is not your reputation but indicates the characters opinion of you, usually starts out neutral and goes up or down as you interact with the characters. I believe it 0 to 100 with zero being hostile and 100 being "admiring". You can raise their opinion by your interactions and by giving them items for nothing and by increasing your reputation. Enter the trade mode and put something in you side and press the check mark. Click yes and you will slowly increase their opinion of you which, along with reputation, will bring the prices down.

Thanks for the information. It turned out to be a display bug, the trader's gold wasn't appearing so I didn't know that he didn't have enough to cover the cost of the item I was selling. This has since fixed itself.

You're welcome, thanks for pointing that out, I will update the images to indicate the merchant must have enough gold to purchase your items . . .=)

Thanks for updating this. One minor point though (which confused me at first), I believe that the arrow you refer to as gold is the total worth of all items that the trader has (I assumed that was his gold at first and so couldn't understand why he wasn't paying). The gold itself is within the trader's inventory. I think we can agree that it is a most confusing way of presenting things!

You are correct, thanks again for you input, I was too quick in adding that. I will fix it shortly . . .=)

Thought I'd add a little bit here after playing for a bit. Hopefully this hasn't already been covered....
You get more money for the items you sell if they are repaired. With one level of repair (60% fix), you can turn a 3/19 item into a 'repaired' 11/19 item and will receive a bit more money for doing so. You get more money still if it's fully repaired, so it may worth it to have the shopkeeper repair the item before you sell it, especially if the item is already worth a lot of cash. I tried it out with a plain sword. At 3/19 it was 583 gold, 11/19 was 795 gold, and 19/19 was 1008 gold. It wasn't worth it to have the trader repair it from 11 to 19 since the repair itself cost more than the gain in selling price;