When one performs Netilat Yadayim before eating bread, he must wash his hands with a utensil. Our hand washing is modeled after the washing of the Kohanim in the Bet Hamikdash, which was done from the Kiyor (sink) in the entrance to the Temple. Just as the Kohanim had to wash with a utensil, similarly, we must wash our hands with a utensil before eating bread.
The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), in Parashat Tazria (12), addresses the case of a person who has no utensil for Netilat Yadayim. He writes that a person in this situation can perform Netilat Yadayim by dipping his hands into either a natural body of water (like a river) or into a proper Mikveh. Strictly speaking, a person who performs Netilat Yadayim in this fashion needs only to dip his hands in the water once, and then remove them and recite the Beracha. However, the Ben Ish Hai writes that according to Kabbalistic teaching, one should dip his hands in the water three times, and then rub them together to dry them before reciting the Beracha.
Later, in Parashat Kedoshim (18), the Ben Ish Hai discusses the case of a person who has no water for Netilat Yadayim, but does have access to other liquids. He writes that although one should not, as a rule, use liquids other than water for Netilat Yadayim, under extenuating circumstances, where water is unavailable, one may use other beverages. However, the Ben Ish Hai adds, one does not recite a Beracha when performing Netilat Yadayim with liquids other than water.
The Shulhan Aruch allows using hot water for Netilat Yadayim, even if the water is at or above the temperature of "Kereso Shel Tinok Nichvet" (where an infant’s belly would burn on contact). The Ben Ish Hai, however, rules that given the difference of opinion among the Halachic authorities on this issue, one should preferably not use hot water for Netilat Yadayim. If one has only hot water he should wait for the water to cool before performing Netilat Yadayim. Under extenuating circumstances, when one cannot wait for the water to cool, he may use the hot water, but without reciting the Beracha.
The Ben Ish Hai adds a warning that elderly people who prefer using warm water for Netilat Yadayim must ensure that the water is lukewarm, and not hot.
Summary: One must wash Netilat Yadayim with a utensil, rather than by simply putting his hands under running water. Alternatively, one can dip his hands into a natural body of water or a proper Mikveh. Liquids other than water should not be used for Netilat Yadayim; they may be used under extenuating circumstances, but without a Beracha. Similarly, hot water should not be used for Netilat Yadayim, and should instead be allowed to cool. Under extenuating circumstances, hot water may be used but without a Beracha.