There are several night trains each day from and to Hanoi (about 9h, ca. 20$ for a soft sleeper depending on the train).
Everything you will see is either water or land. The place is a dry old mainland.
There are a couple of ATMs in Lao Cai. The Techcom Bank has ATMs on the square of the train station as well as close to the border. However, they accept only some international cards. There is one ATM accepting all international cards but it's neither close to the border nor to the railway station. Motorbike drivers usually know it and will drive you there (one-way 10'000d)
As soon as you leave the immigration building you will be approached by money changers. They usually offer poorer exchange rates than the bank. There are two banks just next to the border and a third one just at the other end of the first bridge, though these are all annoyingly closed at weekends. Banks in Hanoi will also readily exchange your RMB for Dongs.
You can get free wifi near bus/train station at the Fansipang restaurant and Le Bordeaux restaurant, both are visible from station.
Trains run from the train station in Lao Cai to Hanoi - with the option of an overnight sleeper. This will however put you in Hanoi rather early with the only company being a million motorcycle and taxi touts. So its generally a good idea to have a plan as to where you'll be heading to on arrival to avoid being scammed. Prices for a soft sleeper ticket are around 300,000 dong, lower classes are cheaper. Check http://www.seat61.com/Vietnam.htm for up to date information on prices.
Train Company - Livitrans
There is also a bus service to Hanoi costing 89,000 dong.
Night bus to Hanoi. Costs about 150000 dongs. Very uncomfortable with loud music and no leg space. Train is much better option, but often need to be booked in advance.
Minibuses run from outside the chinese Hekou border immigration exit, and train station straight up the mountain. Cost should be 25,000d per person and the bus leaves only when it is full.
If arriving via the chinese Hekou border, watch out for touts who will persistently attempt to get you to pay anything up to 150,000d, or ¥20 (approx 50,000d) per person to get to Sapa. Just ignore them and walk to a main street and flag a minibus with a sign showing Sa Pa at the windscreen. Confirm with the driver or bus attendant 25,000d and hop into the minibus to Sapa.
If arriving by train (usually at around 5am - 6am) watch out for minibus scams asking for 200,000 dong upwards. Generally they can still be bargained down (despite much disgust from whoever is so kindly scamming you).
Yunnan Province, China
about 40min walk from bus+train station, is the border crossing to Hekou in China. Border office is a big building next to a bridge, opposite Sapaly hotel / Biti's trade center. From here you can catch an onward bus through to Kunming for around Y120.