MDI works on the principle of two different insulins, basal and bolus.
The basal insulin (lantus or levemir usually) is sometimes known as your background insulin and is taken once or twice daily (depending on how long it 'lasts' in an individual etc). The basal insulin should deal with the background level of glucose the liver gives off, so the theory being that if the basal dose is right your levels should stay steady without eating/unusual exercise. However, not everyone finds they have a steady need for the same level of basal all day so there may be fluctuations, to varying degrees and this to me is the key advantage of a pump in that you can have different basals throughout the day as mdi only gives you the chance to change it on your once or twice daily injection.
The bolus element of the regieme is there to deal with your intake of carbs. To do this you need two things; to know the carb content of the food and your insulin to carb ratio. Carb counting seems extremely daunting at first but it does become second nature very quickly. In some areas you may be able to go on a course to learn, or if not you should be able to have some sessions with a dietician. The insulin to carb ratio is in many ways trial and error, although there are sone calculations based on weight etc that can be a starting point. Many people need different ratios at different times of the day, in most cases (not all), insulin resistance is higher in the morning so more insulin may be required per gram of carb. With the above worked out it's then a case of injecting everytime you're eating carbs, including snacks if applicable!
On the surface mdi does seem extremely complicated but in reality it does become quite natural quite quickly. Good luck if you do choose to try it!