There are many package trips which offer flights, hotel, and a Northern Lights tour. Be aware that various factors influence your likelihood of seeing the Northern Lights (or aurora borealis). First of all, don’t visit in summer! Night doesn’t fall in Iceland in the height of summer, there is just twilight for a few hours, so the aurora is not visible. The best time to go is between October and March. Secondly, cloud cover may obviously limit visibility, but Icelandic weather is very variable so clouds may not be set for the whole night. Finally, the aurora varies in strength, so keep an eye on the aurora forecast (http://en.vedur.is/weather/forecasts/aurora/) which gives a rating between 0 and 9 for the strength of the aurora each night. The good news is that most tours will take you out again for free if you don’t see the lights on your first night.
If you go on an aurora tour, be prepared for a coach trip lasting an hour or more as you are taken away from the city lights. Take warm clothes. You will likely be taken to a location near a café, so you can visit the restrooms and buy a hot drink, but this isn’t guaranteed. The coach will have a guide who will hopefully keep you entertained with tales of Iceland and the science of the Northern Lights, and you’ll likely get back to your hotel around 1-2am, depending on the aurora conditions.