There's already been good advice. Unless your monitor comes with some proprietary software, like my NEC 3090 does (Spectraview II), your best bet is to use something from Xrite or similar brand to calibrate your monitor. There are two types of instruments that will do the job - a colorimeter or spectrophotometer - and which you choose will affect your use options and the price.
The cheaper of the two will usually come with good simple software to profile your monitor or projector or even ambient room light - any device or environment that transmits light. These devices and their associated software can be excellent to set up your monitor. Coloimeters can't accurately calibrate reflected light; only a spectrophotometer can do that and also calibrate transmitted light as well. So, one must buy a system which include a much more expensive spectrophotometer to do both. Xrite sells them in several different packages, each one unlocking different features in the same basic software program, each package level "higher" (in price and designation) allowing you to profile more devices in more specialized ways. For intsance, if you have a "photo" spectrophotometer system, you can profile your monitor and your inkjet printer and paper choices as well, among other capabilities. If you'd care to, you could buy one of the later packages, and have your Fuji printing supplier print out a test pattern, the file for which you provide him, for you to then evaluate and then profile yourself. Then, you could, in turn, present the resullting ICC profile from his test print back to your printer, so that he can use it to dial in your particular print orders. Of course, this assumes that he would have to be amenable to using your profiles just to print your orders.
Another approach also depends on your printer already having an accurate ICC color-controlled workflow himself and his willingness to share his own profiles with you. If he is able and willing, and you have a good and otherwise calibrated (usually set up for sRGB, sometimes for Adobe RGB) monitor plus Photoshop, you can preview how your file will look printed out on his printer by applying his ICC profile to the View menu using the "Custom" Proof Setup command and then viewing the result with the Proof Colors command. If your image, using your printer's profile, looks wrong, you can edit it in photoshop to look correct using the provided ICC profile and save a new and differently named color-correct-looking version of the original file for sending to your outside printer.
This is a big and very complicated subject and requires quite a bit of learning beyond the little I've explained, but I hope I've shed just a little bit more light on the subject than just telling you what colorimeter to buy.