Simple search tasks are incredibly easy to set students using the web as a language-learning tool. They don't have to be particularly complicated, or even well-researched, although this helps!
A simple task I have used with students is to set your students the task of finding out about holiday information, although the same process could be used for just about any type of information, for example buying a car or presents for your family.
Firstly, prepare a worksheet something like this:
The 14th of next month is my girlfriend's birthday. I would like to take her to Rome the weekend afterwards (18th – 20th). Can you find out how much it would cost for two return air fares from London Gatwick? When we get there we need a place to stay, but I don't want to spend more than 100 Euros a night. Can you find a hotel near the city centre? I would also like to find out what plays are on at the theatre …
You could alter this. For example, to review sports vocabulary, you could ask them to find out what sports are popular in your chosen destination.
This can work quite well on its own, but to make it more communicative, get your learners to work in pairs or small groups of three with each group finding out about a different city with a set budget. The class then decide which city would be best – perhaps based on information about your personal tastes and interests, so they have to decide which city break would be best for you.
If you only have one or two devices available for your class, set different students the task over the course of a week before conducting a discussion at the end.
You can control the answers more, and speed up the task by suggesting sites for your students to use, but this may remove a degree of authenticity from the task – most of us, faced with this kind of task in real life, would either use a selection of known names, or go to a directory.