New Zealand favour discipline over aggression
Every team has a certain style of playing cricket and New Zealand's preferred approach in Test cricket is to maintain control over proceedings for extended periods of time. The game might not move much in either direction in that time, but they like it that way. They believe in seizing the advantage bit by bit. If they're able to control the flow of a match for a session or two, they know that they have the game to stretch it further. With bat and ball, most of their players choose discipline over aggression.
Be prepared to play boring cricket
When you encounter a team that plays like New Zealand do, it's important to acknowledge it and change your game slightly too. There are many phases in Test matches when New Zealand's seamers bowl a teasing line outside off with a packed off-side field. The length they use will also be a little shorter than what's ideal for driving, and never short enough that you can score comfortably off the back foot. Barring the first day or so, pitches in New Zealand usually become fairly batting-friendly, with little pace off the surface, which is why their bowlers know to play the holding role effectively. India's batters must respect their strategy and avoid getting too aggressive. A couple of wickets is all it can take to change the course of a Test match.
Bowl bouncers
English conditions typically aren't considered ideal for consistently short-pitched bowling, but if you have the pace, like this Indian bowling attack does, you must use bouncers liberally. The New Zealand batters are unlikely to take them on, but bowling short will be a good ploy to prevent them getting comfortable with planting the front foot and playing the ball close to the body. When you encounter a batting side like New Zealand, it's important to rattle their cage every now and then. While most sides would bowl bouncers to the likes of Ross Taylor and Colin de Grandhomme, the Indian fast bowlers must use them against Henry Nicholls, Devon Conway and Tom Latham too. Also, whenever a batter is new at the crease, there's always a little window of opportunity before he finds his feet, so bouncers are helpful in unsettling them.
Don't overdo the attacking lines and lengths
Apart from Kane Williamson, and perhaps Taylor, the New Zealand batting unit isn't full of batting superstars. Most of them aren't attractive shot-makers who capture the attention of the opposition and viewers alike. Their approach to batting is workmanlike (except perhaps for de Grandhomme): most of them know where their off stump is and happily build their innings on the pillars of either leaving a lot of deliveries alone or playing them really close to the body. The likes of Latham, Conway, Tom Blundell, BJ Watling, and even Williamson to a certain extent, believe in wearing down opposition bowlers. Since they aren't your typical play-on-the-up kind of batter, bowlers are encouraged to bowl a little fuller and straighter to them. While attacking bowling of that sort isn't a bad tactic, it's important India do not overdo it. They need to have patience as a bowling unit. When confronted with defensive batting styles, bowlers are prone to try to produce magic balls, but one must remember that the majority of wickets in Test cricket fall to "normal" deliveries and it's the pressure of persistent efforts that produces mistakes. Counter discipline with discipline and see who blinks first.
Aakash Chopra puts together his Indian team for the World Test Championship final
Crucial runs might come from the lower half of the batting order
India and New Zealand possess great fast-bowling line-ups (and I'm not using "great" lightly here). Considering the pedigree of the two attacks, it's almost a given that both will make early inroads and pick up wickets at regular intervals. While most batting innings are built around one or two big innings, there's a strong possibility that might not happen in Southampton, so it's important to stay in the contest even when the lower order is out in the middle, batting. English conditions, with all the green and moisture around, are conducive to traditional orthodox swing bowling but not so much reverse swing. Add to that the fact that none of the New Zealand bowlers are rapid and it presents the Indian lower order the opportunity to contribute significantly, which they must seize.