Grip
Grip is often overlooked when putting but how you hold the disc and its orientation in your hand have significant affects on the trajectory, spin, and repeatability of your putt.
I recommend using a grip that has all 4 fingers under the disc and at least 2 fingers extended out under the flight plate. The grips that fit this bill are the fan grip that has the index finger and pinkey on the rim and the middle and ring fingers under the flight plate or a grip that has only the index finger on the rim and the other 3 fingers under the flight plate. The fingers under the flight plate will give you greater contol over the disc angle as well as increase your "touch" on putts. Thumb placement should somewhat oppose the index finger and whatever is comfortable should work but I recommend avoiding having your thumb too close to the center or edge of the disc. Your grip should be firm but not overly tight and your wrist should be loose enough to sway freely. I do not recommend grips without the index finger under the rim as they often lead to consistency problems with off axis torque and not generating enough rotation to keep the disc flying without wobble.
A good sign that your grip is stable and in a position to get a clean release with maximum control is if you can lift your thumb off the disc and still hold the disc and vary its angle.
The orientation of your grip is also very important in terms of controlling and repeating your putt. I recommend orienting your grip somewhere between 2:30-3:30 on the disc. This is a fairly wrist neutral grip that gives the greatest freedom of angle adjustment and you can make adjustments as you see necessary. Open wrist grips at 4:00 or lower will generate less spin and have a greater nose-down tendencies. Loft putts and hyzer putts are also easier with this grip orientation. Closed wrist grips at 2:00 or higher generate more spin and make it easier to keep the disc level both in hyzer/anhyzer and nose up/down terms. While this may seem advantageous, a closed wrist grip gives the least freedom to adjust angles and is the most difficult to repeat as it requires a very quick motion to get a clean release. If your putting motion is too slow there will be a tendency to pull the disc to the right. For the sake of repeatability and on a basis of strengths and weaknesses, a neutral wrist grip should be the best choice for most players.
Finger Spring
The clean line, finesse, and rotation of this putt are the result of the spring of the fingers off the disc. The spring is actively removing all of the fingers leaving the disc at the same time. This is similar to throwing a dart. A uniform dart throw requires all of the fingers to leave their pressure points at the same time. A clean putt release will have the same requirement. The spin needed to keep the disc flying without wobble is generated by the slight tension of the fingers "popping" off the disc while the disc is being accelerated forward. Your hand should finish fully open. While this may take some practice to perfect, a good release should occur somewhere near the top of the stomach while feeling very clean and the disc will hold a tight line with some rotation and no wobble. The spring of the fingers is one of the most important parts of the putt.
To be a little more explicit, the spring of the fingers is achieved by actively letting go of the disc but making sure that all of your fingers leave the disc at the same time.
The entire range of motion covered before you physically release the disc by actively springing your fingers off the disc will be small. The disc will only cover 12-18" of distance before you release the disc. The entire motion needs to happen very quickly. The compact motion powering the disc is what separates this form from the elongated stroke and slower motion of the long-arm putt.