Ok I'm going to very generic here to not veer into medical advice (this is what I do, I'm a nutritionist).
Plan how long you want to detox for - 3 days, 7 days, 10 days, etc.
If its 3 days, no sweat, pretty much cut out/eat whatever you want. But if its longer (7+ days) plan it out and cut things out in food groups. For example (emphasized because this is just a suggestion/sample detox plan, you can amend to your needs/lifestyle, etc) day 1 cut out caffeine, sweeteners, and processed food (processed food is pretty much anything pre-packaged). Day 2 cut out meat & poultry & eggs (and all of day 1 stuff). Day 3 cut out fish and dairy (and all of days 1 & 2 stuff). Day 4 cut out processed grains (wheat products, white rice, oatmeal, grits/polenta, etc) and all of days 1, 2 & 3 stuff. Day 5 cut out nuts and nightshade vegetables as well as previous days stuff. Maintain this restricted diet for 2-5 days, then slowly, one food group at a time, reintroduce foods.
Do not plan to live long term on a detox diet - if you want to go vegan, etc there are long term dietary needs that need to be addressed. Do take a few minutes each day to take note of how you feel in a journal or even just on a piece of paper - tired? Energized? Headaches? Gassy? Refreshed? How does your skin feel? Are your bowel movements noticeably different? Are you more/less hungry then usual? Etc.
Obviously if you have anything else going on (diabetes, pregnancy, digestive disease, chronic inflammation, are a minor/still growing, anything, etc) or any concerns speak to a doctor before embarking on a detox.
You might want to ease up on your exercise regimen, if you have one, during your detox. You might also want to add to the detox process something like a steam and/or massage, or yoga.
Some people start their detox days with a shot of 1 tbsp olive oil & 1 tbsp fresh squeezed lemon juice (one lemons worth).