The wise guy answer is that you need AAS or ICP equipment. These are, of course, incredibly expensive, take up a lot of room etc.
First, some perspective. It isn't necessary or possible to practically 'dial in exactly' by measurement and adjustment. You will get a pretty good beer if your ion contents are only approximately the same as those you will find associated with the style in various sources. The 'dialing in' is done by using that piece of equipment which is orders of magnitude more intricate than AAS or ICP machines: your palate. You can measure to 0.1% and make additions to the same level of accuracy and will still need to do that last step to get the beer you really like.
The important thing is to get to the approximate ion concentrations. How do we do that? Far and away the easiest method is to start with water that has no ions in it and add the stuff you need to get the ions you want. This is quite easy to do and requires nothing more in equipment than an accurate scale to weigh salts, a supply of those salts and a source of water with no ions in it. Such water can be obtained from health food stores and drug stores but most ardent brewers wind up installing an RO unit. You will also need a means for calculating the salts required to match an ion profile. There are several calculators out there that will do that. None of them appear to be very good but you don't need 'very good' to get into the ballpark.
The other route is to accurately characterize your source water and fiddle with it to get the ion profile you want. If you get it from a municipal supply you will get from them annual water reports of varying degree of value. Some will give yearly averages and some detailed month to month data. If you are on a well then you will have to get the water analyzed or analyze it yourself. Many guys just send a sample off to Ward Labs which provides good service to home brewers at a very reasonable price. The catch in this approach is that what comes out of your tap can vary over the course of time. Sometimes this variation is minimal and sometimes it is dramatic (where municipalities may switch sources or blend sources in different ratios depending on weather, demand etc.). Note that with an RO sytem not only is the mineral content suppressed but so is the variation in it.
The most difficult and time consuming approach is to make measurements on the water itself. This can range from the use of a simple drop count alkalinity test designed for aquarium or swimming pool owners, to inclusion of another drop count test for hardness to spectrophotometer based tests for chloride and sulfate to ion selective electrode tests for sodium. Clearly there is a progression in cost and the time required.
If you read here a bit you will soon get an appreciation for what home brewers do with regard to this question. This may help you to grasp what is necessary, unnecessary, practical, simple, inexpensive etc. You will probably wind up with an RO system.