First of all you need to have your screen calibrated and profiled. That's essential. Unless your screen is accurate whatever you do with the printer is going to be a waste of time.
Once the screen is calibrated and profiled you can now look at the printer.
You have a number of options.
You could use the paper manufacturers default profiles for the printer/ink/paper combinations you are using. These I have found can be variable,some are good some are not so good. But they are free.
You can pay to have custom profiles made. This may be necessary, as the "canned" profiles may not be good enough or the printing combination you are using may not have profiles available. There are several companies that will produce profiles for you, some make no charge ,if for example ,you purchased your printing materials from them .On the other hand if you have to pay they can cost between £15-£25 each depending on the company. Often this can be the cheapest option. ( Apart from the Free ones).
Finally you can produce your own. This is not a particularly difficult job , but you do need the right equipment and software to do it. You could look at the ColorMunki from X-Rite. This device calibrates your monitor and will produce profiles for you printer. it does however have a price tag of around £300.00. There are of course more expensive options out there, but I suspect for most people the ColorMunki may be the option they will go for.
How do you know the colour are correct, well that's what this whole procedure is about. Ensuring that the screen and prints match.
My monitor is calibrated and using the suitable profiles for my printer I get an excellent screen to print match.
Hope this helps