The basic methods currently in use are slack / layout method and tension method, but they are invariably modified to site conditions such as landscape, weather, available equipment etc.

Slack  method / layout method
Using this method, the conductor is payed off along the ground by means of a pulling vehicle . Reel is placed on reel stand on the ground designed for supporting the reel on a spindle passed through arbor hole.  Alternatively,  the reel is carried along the line on a vehicle and the conductor is deposited on the ground. Reels are positioned on reel stands, Usually, a braking system is provided to prevent overrunning and backlash. When the conductor reaches a supporting structure, pulling is stopped and the conductor is placed in travelers attached to the structure before proceeding to the next structure
There is a very high probability of surface condition of the conductor being damaged when this type of stringing method is used.

Tension method
This method is used to keep conductor surface safe during stringing process. In this method, the conductor is kept under  tension during the stringing process  to keep the conductor clear of the ground.  A pulling  line is initially pulled into the travelers which is then used to pull the conductor from the reel stands using specially designed tensioners and pullers.

Grounding
Adequate grounding should  be established at construction  work areas prior to stringing. The equipment used  and methods followed should be based considering exposure to maximum system electrical hazards and soil conditions at the site so that  a safe environment for the transmission line construction workers can be provided.  All equipment, conductors, anchors, and structures within a defined work area must be bonded together and connected to the ground electrode for establishment of equi -potential work zones to limit touch and step voltage to a safe level.  Workmen should be given adequate training regarding safety standards at construction site.

Tensioner bull wheel characteristics
Semicircular grooves with depths in the order of 0.5 or more times the conductor diameter and with flare angles in the order of 5° to 15° from the vertical generally have been found  to be satisfactory for stringing.  The number of grooves in the bullwheel must be sufficient to prevent the outer layer of wires of multilayer conductors from slipping over underlying layers.   In order to avoid loosening of outer layer of strands as it passes on bull wheel, for normal conductors having a right-hand direction of lay for the outer wires, bull wheels should be arranged so that, when facing in the direction of pull, the conductor will enter the bull wheel on the left and pull off from the right side and will enter the bull wheel on the right and pull off from the left  side for normal conductor with outer layer having left had direction of lay.
The material and finish of the grooves must be such as not to damage the surface of the conductor.

Puller and tensioner operating characteristics
There are basically two types of pulling machines used in the construction of transmission lines being strung under  tension. These are defined as bullwheel and drum/reel-type.  Pullers should be equipped with load-indicating and load-limiting devices.  Tensioners should be equipped with tension indicating devices.  The capacities of the puller and tensioner should be based on the conductor, span length, terrain, and clearances required above obstructions. Sag tensions should never be exceeded during stringing. Required capacity for both puller and tensioner can be calculated as mentioned in IEE 524. 
Positive braking systems are required for pullers and tensioners to maintain conductor tension when
pulling is stopped.  The pulling and braking systems should operate smoothly and should not cause any sudden jerking or bouncing of the conductor.

Travelers 
The selection, design and use of travelers used in the stringing process of the conductor are to be in line with recommendations of IEEE 524. 

Stringing operation
The selection of site for various equipment for stringing procedure should consider accessibility, terrain, angles in the pull section, location of usable deadends, length of conductor to be strung, available conductor and line lengths, puller capacity, snub structure loads, the physical area needed for placement of the equipment, and the ability to provide an adequate grounding system.
It is recommended that matched set of conductor be used in a given pull, and preferably in any given sagging section. This will help avoid significantly different conductor sag characteristics.
Attachment of the conductor to the pulling line, to the running board, or to another reel of conductor to be pulled successively is accomplished by the use of woven wire grips. These grips should be of compatible strength and sized to the conductor or pulling line on which they are used.
The overall diameter of the grip, when placed over the conductor or rope, should be small enough to pass over the sheaves without causing damage to the sheave or its lining. The grip should also be capable of connecting with a proper size swivel link.  Metal bands should be installed over the grip to prevent it from accidentally coming off and dropping  the conductor. Pulling speed is an important factor in achieving a smooth stringing operation.  Slower speeds may cause significant swinging of the traveler and insulator hardware assemblies. Higher speeds create a potential hazard of greater damage in case of a malfunction.
The maximum tension imposed on a conductor during stringing operations should not exceed that necessary to clear obstructions on the ground.
Light and steady back tension  should be maintained on the conductor reels at all times to prevent over-run in case of a sudden stop.  It is required  to periodically loosen the brake on the reel stand as the conductor is payed off. As the reel empties,  the tension rises  since the moment arm available to overcome the brake drag is reduced, causing the conductor to wedge into the underlying layers on the reel. The reel should be positioned so that it will rotate in the same direction as the bullwheels.
Birdcaging in conductor during stringing can be avoided  by allowing enough distance between the reel and tensioner to permit the strand looseness to distribute along the intervening length of conductor and simultaneously maintaining enough back tension on the reel to stretch the core  and  inner strands to sufficiently tighten the outer strands
Conductor should not be strung if adverse weather is predicted before the entire sequence can be completed.
Conductor mid span and end joints should be done using correct fittings and practice as recommended by the fitting manufacturer.