Forget 'direct copy'. Import your image into a decent image processing program and check what it looks like on screen first. (Tweak as required).
Matching screen colours (made up of transmitted light) to print colours (made up of reflected light) is extremely difficult. Assuming that you've checked that your monitor is correctly set up, so that you're seeing 'true' colours in the first place, the most likely problems are:
(a) using poor quality inks ;
(b) using poor quality paper ; or
(c) failing to set the printer to match the paper.
I'll assume that you're using decent inks (either Kodak originals or reputable third party inks), so that means considering the paper quality. (In my experience, the quality of the paper used is about a thousand times more important than the quality of the inks). If you're using cheap supermarket stuff, bin it! Try some Kodak Ultra Premium Photo Paper or, if you really have to use supermarket stuff, Tesco 'Finest' Photo Paper.
Once you've got hold of some good quality photo paper, read the leaflet that should have come with it, telling you the settings you need to use with your printer. (They're not always the ones which you'd guess at!). Then, when you select the 'Print' option from your image processing program, don't just click on 'OK'. Click 'Properties' and check that the settings shown are the ones indicated by the manufacturer of the paper.
Chris
PS: If you've not checked your monitor set up, go here
http://reeddesign.co.uk/testcard.htm
and check that the numbers 0 to 10 are visible on both lines. (If they're not, follow the instructions to adjust your monitor).