The easiest way to reach Almaty is by air. A detailed information about flights to/from Almaty can be found on the Web page of Almaty Airport. The main conference hotel Astana and some other Almaty hotels arrange transfer from/to the airport. If your hotel does not provide transfer, LPAR will arrange transfer from the airport.
You need a valid visa to travel to Kazakhstan. Some information on visa application can be found in eXpat.kz Web pages. To apply for a visa, LPAR participants need an official invitation issued by Al-Farabi Kazakh State National University or by the Academy of Sciences. To obtain such an invitation, please fill out the visa information form and send it to the local organizers of LPAR at email@example.com. You will then receive an invitation (it may take a few days), with which you can contact the appropriate consulate of Kazakhstan, see the list of Kazakhstan embassies and consulates for an appropriate embassy.
LPAR made an arrangement about special discount rates with the hotel Astana, see information on conference venue.
There are many currency exhange offices, some of them are open 24 hours a day. Euro, US dollar, Russian ruble, and Turkish lira are accepted essentially in all offices at competitive rates. I would not recommend to take other currencies, for example I had a hard time trying to get a good rate on UK pounds (some offices offered rates 25% below the official one!) There are many cashpoints accepting all major systems, however, not all of them are functioning perfectly.
Almaty is a beautiful city. When I was there, I prefered to travel on foot as much as possible, even very late at night. If the distance is large, take a taxi. The price should be negotiated in advance (probably in writing, since the drivers usually speak only Russian.) I found the drivers very friendly and ready to answer your questions (but see the above remark about the language...) The best way to know the prices is to ask local organizers. Normally, the prices are between 0.7 and 2 Euro. Private cars also act as taxis. It is, however, not recommended to travel from the airport on your own: taxi drivers will try to rip you off at around 50 Euro, and you will discover that there is only one driver who delivers to your hotel.