Annemasse  is a city in the Haute-Savoie region of France, located directly across the border from Geneva, Switzerland. Many of its inhabitants work in Geneva and travel home every day. It is a useful place to stay for those who find Geneva's hotel prices too much for their pocket.
From Geneva by public transport
Annemasse is bordering the larger city of Geneva, on the Swiss side. There are several different connections, but they might be difficult to find, especially if you don't speak French. Chêne-Bourg station in the east of the Geneva is the terminus of Annemasse's public bus company's  line number 1. From Moillesulaz, the terminus of tram 12, you can walk over the border and take either that same bus or number 2. If you feel like walking, another option is to walk from the border to the city center, a distance of about 2,5 kilometers (1,5 miles).
If you are taking the bus you should better have a map of the bus network (the part of Annemasse's bus network you need to get in is also on Geneva's public transportation map) and preferably also a good map of the city itself. Take notice of the names of the bus stops, because the buses continue to the other side of the city... in the worst case you might end up in an industrial area in the middle of nowhere.
Annemasse is easily reached from Geneva and elsewhere in the region if you have a car.
The railway station is located north of the city center. Trains arrive from Lyon, Chambéry and other places in France. The line to Geneva Eaux-Vives and Chêne-Bourg is not currently operational. A new local train network connecting the cities in the region is under construction and is planned to open in 2018.
The city center is not very large, so you can walk around by foot.
The only form of public transportation is the bus network, although most visitors probably will use it just for transportation from Geneva and back. A single ticket costs 1,30€ and is valid for one hour. Tickets are bought from the driver, and you'd better have exact change (and Swiss francs are not accepted). On Sundays and other holidays there are just two lines that run, DA and DB that are drawn on a separate map on the bus stops.
Frankly speaking, Annemasse is for the most part just a bedroom community of Geneva, but there are still a few things to experience.
If you're staying for a longer period in Geneva, Annemasse is a good place to buy food and other necessities cheaper than in Switzerland. The city is not a major shopping destination, though. There is a Casino food store along the main road at about 10 minutes walk from the Moillesulaz border station, and a smaller SPAR closer to the border.
There is a cheap but good Ibis Budget hotel in Annemasse, starting from 49 euros (in high season 57 euros) for a 2 person room.
Basically you have the same options as getting in. Geneva is nearby and trains take you into France.