Where and how do they get their food?
More importantly, where do they get money to buy stuff? Is this by tax from the people who stay at the gift?
The Night's Watch used to collect taxes and farm areas near the Wall. But recently, there have been several wildlings' raids and people have moved south; thus there aren't a lot of taxes and they can't afford to have all 19 castles of the Wall that there used to be (also there is a lack of men).
A Storm of Swords, Chapter 40 (Bran):
The Gift is a tract of land measuring twenty-five leagues southward from the Wall that the Night's Watch received from King Brandon Stark of the North. For years the Watch farmed the Gift, but as their numbers dwindled there were fewer hands to plow the fields, tend the bees and plant the orchards, so the wild reclaimed much of the area. Wishing to restore the Night's Watch and reward its loyal service in defense of the realm, Queen Alysanne, wife of King Jaehaerys the Conciliator, doubled the extent of the Gift. Towns and villages that were located within the "New Gift" supported the Night's Watch with their taxes, rendered by goods and labor. In time, the New Gift lost population as people moved south, into the mountains or into the Umber lands east of the Kingsroad to avoid wildling raids, further reducing the support structure for the Night's Watch and the Wall.
The Night's Watch has several iron smiths etc. These are the the people that are making the weapons of the Brothers
That's right. The first gift was given to the Night's Watch by the Starks, and this was farmed by the Night's Watch to supply them with food and materials. Later, the Gift was extended to encompass several towns, which pay taxes to the Watch.
As I remember it, Benjen Stark travels to King's Landing to ask the king for money and new recruits (prisoners are given a pardon in exchange for taking the black). It seemed to me, to be common practice.