There are circuits out there - some simple, some not so simple, that will do what you want - maybe. You said 88 to 108 mHz but you didn't say FM, AM, SSB, digital, etc. Usually when someone mentions that band they mean FM. Note that FM broadcast deviation is different than for voice communications.
You could look to Ramsey electronics for kits. I know Ocean State Electronics, among others, sells educational kits that appear excellent for learning. I suppose you could get the schematic for those and start there. As others have already indicated, lowest cost approach might be to purchase the item - but that's only if what you can purchase is what you need.