Just so there is something concrete to discuss, say I have this color scheme:
There are many articles about how to pick a coherent color scheme based on complementary colors, monochromatic colors, etc. however, once I have a set of colors, how do I decide which color is the header, which color is link, which is background and text. Even if I decide that I want a light on dark or dark on light scheme, putting rest of the colors on screen can still make the site look ugly.
Are there rules of thumb or general guidelines that help one decide which colors go where?
I see a lot of people commenting things like "there's no right answer" which I (sort of) disagree with... There's certainly at least one right answer, maybe a few and I'm sure there's a bunch of wrong answers too, good design is about reaching the best possible solution based on the resources and time available to you And surely such a solution is going to outweigh several alternatives. You've given us a colour palette for the purposes of discussion so, I'm going to do just that and answer your question based on the supplied colour palette. (Given I haven't seen the layout you're working with this is still gonna be pretty broad but it'll have some process for you to follow.)
So, the first colours I like to pick when creating a colour scheme in a web project are the background for the body and the main text colour. It's normally a good idea to pick the two most contrasting colours to fill these roles and your example palette is no exception so in this case the colours are #DEE1DD and #28363D. Now we have to decide which to use for the text and which to use for the background and in most cases I try to use the lighter colour for the background and the darker for the text. There's been considerable research to show we read a dark colour on a light colour more easily than a light colour on dark so that's what I generally default to unless there's a reason for a darker look (like you're doing a website for a heavy metal band or something... I'm gonna assume that's not the case here). So, the background to our body will be #DEE1DD and the text colour will be #28363D.
Next I like to move on to what I think is the next most important item, which is hyperlinks. You want a colour that contrasts enough from the background as to not be difficult to read but also contrasts enough from the text in order to be noticeable. In this example most of the lighter greens will be illegible on the light background so the most obvious answer is #2F575D.
Next you alluded to a header that needed to be coloured, and again we need it to contrast from the background. In the interest of minimalism I try and reuse the colours I've already used in the body, and in this case the text colour is probably too dark to be filling large amounts of space so I'd be inclined to aelect #2F575D and for all of the above reasons I'd use the background body colour #DEE1DD To fill in any text or links in the header.
Finally I cover non essential design elements like hover states last and we've got a few different greens left to pick from. Again this probably needs to contrast from the background enough as the links don't disappear when rolling over them so if be inclined to go with #658B6F ...
And ... Voila! You now have a (basic) 4 colour scheme. I hope this process helps you as much as it helps me :) !