The basic principle of an elimination programme is to remove from your environment, as far as is practicable, the things that you suspect of causing reactions. You then monitor your symptoms and see if they improve after a period of time. If you want to confirm the results of the trial, you can then reintroduce the substances or start using them again. You do this with care, monitoring your symptoms as you do it.
To make the programme work, you have to be thorough and you have to be systematic. You also have to be patient and to give things time to settle before you make a judgement. It is better to eliminate only one group of substances at a time, say only foods, only house dust mites, or only chemicals, and do it thoroughly, rather than to try several things at once and only do each partially. People often start by doing the latter because it seems less work and they hope it will be sufficient to make them feel better.
If you have only mild allergies or sensitivities, a partial approach will work well. However, if you are significantly affected by your reactions or if you have multiple sensitivity, most people find that the only way to work out what affects them is to eliminate one thing at a time, and to do it wholeheartedly. Although it appears more work, it is shorter in the long run and less confusing.
Choose yourself which approach you will adopt. Whichever way you go, keep an open mind as you go along, monitor symptoms carefully and retest things whenever you are not sure.