How do I string a low voltage wire between two buildings?
For network communications, you'll want to look at article 830 in the National Electrical Code (NEC).
Circuit Power
For what type of cable to use outside and entering the building, 830.40(A) and (B) list the type of cable based on the application.  Before you can determine what type of cable is appropriate, you'll have to determine if you have a low- or medium-power circuit. For this, you'll look at Table 830.15.



Cable Type
Once you've determined if you're dealing with medium- or low-power circuits, 830.40 tells you what type of cable you can use.  For medium-power circuits, you should use type BMU, BM, or BMR. For low-power circuits, you should use BLU, BLX or you can substitute cable types based on Table 830.154.



Location and Clearances
Since the cable will be run from building to building in the air, 830.44(A)-(I) should be followed.
Sections A-C deal with keeping network-powered broadband communication cables away from electric light, power, Class 1, and non-power-limited fire alarm circuit conductors.  This basically says that the network cable should be below these other types of cables, and that they should be kept away to avoid accidental contact.
Section D specifies clearances from ground (ground ground, not electrical ground), and says.


2.9 m (9.5 ft) — above finished grade, sidewalks, or from any platform or projection from which they might be reached and accessible to pedestrians only
3.5 m (11.5 ft)—over residential property and driveways, and those commercial areas not subject to truck traffic
4.7 m (15.5 ft) — over public streets, alleys, roads, parking areas subject to truck traffic, driveways on other than residential property, and other land traversed by vehicles such as cultivated, grazing, forest, and orchard


Section E says that if you're going over a pool, use the clearances specified in 680.8.
Section F calls for 2.5 m (8 ft) clearance, from any roof the cable passes over.
Section G says that if your cables do not have an outer jacket, don't attach them to a building within 900 mm (3 ft) of windows that open, doors, porches, balconies, ladders, fire escapes, or similar locations.
Section H says that the cable and supports shall have sufficient strength to withstand the loads to which they may be subjected. There is an exception that says if the cable is not sufficient to be self supporting, it can be attached to a messenger cable.
Section I specifies the minimum distance broadband communications cables should be kept from other conductors on buildings.

(1) Electric Light or Power. The network-powered broadband communications cable shall have a separation of at least 100 mm (4
in.) from electric light, power, Class 1, or non–power-limited fire
alarm circuit conductors not in raceway or cable, or be permanently
separated from conductors of the other system by a continuous and
firmly fixed nonconductor in addition to the insulation on the wires.
(2) Other Communications Systems. Network-powered broadband communications cables shall be installed so that there will be no
unnecessary interference in the maintenance of the separate systems.
In no case shall the conductors, cables, messenger strand, or
equipment of one system cause abrasion to the conductors, cables,
messenger strand, or equipment of any other system.
(3) Lightning Conductors. Where practicable, a separation of at least 1.8 m (6 ft) shall be maintained between any network-powered
broadband communications cable and lightning conductors.
(4) Protection from Damage. Network-powered broadband communications cables attached to buildings and located within 2.5 m
(8 ft) of finished grade shall be protected by enclosures, raceways,
or other approved means.

Grounding
Grounding is covered by 830.100, and says:

Grounding conductor shall be insulated and listed.
Grounding conductor shall be copper or other corrosion-resistant conductive material.
Grounding conductor shall not be smaller than 14 AWG.
Grounding conductor shall not be longer than 6.0 m (20 ft).
Grounding conductor shall be run in as straight a line as possible.
Grounding conductor shall be protected from physical damage.
Grounding conductor shall be connected to the grounding electrode in compliance with 250.70.