This is kind of broad, but anybody with sufficient modern scientific knowledge and modern combat tactics can potentially determine the outcome of any battle in the medieval times.
While the possibilities are almost endless, here are some which I thought would be the easiest and the most effective.
1- Use historical knowledge and battle specifics
Someone from our times would know the details about the particular battle and how the armies were arranged, which weapons were used and what were the strengths and weaknesses of each side. With this hindsight knowledge, you can easily overcome your party's weaknesses and focus on the weaknesses of your foe. Knowledge is power, and future knowledge is like nuclear power!
2- Utilize biochemical weapons to decimate and demoralize the enemy
You have lots and lots and lots of options here. Coat your arrows and spears with venom collected from snakes, scorpions, spiders, poison dart frogs (central and South America only) and hornets. For mineral toxins to coat your blades, use corrosive sublimate (HgCl$_2$), phosphorous salts and sulfide salts. In plant poisons, you can use oleander, calotropis, digitalis, bushman's poison, strychnos, datura, rosary pea, wolfsbane, hemlock ... (and a couple dozen others. I think the point has been made)
3- Utilize wind!
Before the battle, when the armies are camped in front of each other, if the wind is blowing from your side to them, burn noxious chemicals so that the fumes are blown toward your enemy, causing damage and panic. Large torches, coated with a mixture of crude oil, sulfur and powdered oleander will do the job nicely. The fumes will be acidic and toxic, not only inducing cough and teary eyes, but also causing panic and decrease the morale of the enemy.
4- Use blinding beam to disorient your enemy
You would need many mirrors of 1 square foot size. Install the army of these mirror holders (about 300 of these will do) at some out-of-reach location (e.g. at the top of a very steep hill). They will focus the reflected sunlight beam at the enemy's soldiers (specifically targetting archers and cavalry). While they will not be able to set anyone on fire or inflict severe burns, they will be able to blind them and create panic and disorientation, helping your side.
5- Implant poison coated punji sticks in the way of your enemy
I mean these.
Considering that you (the time traveller) in hindsight, knows which path the enemy will take to the battlefield, you can easily deploy tens of thousands of these pointed sticks with poisoned tips, in his way. You can plant them in the jungles and woods in his path and you can lay punji traps for him, by digging up pits, planting punji sticks in them and then covering up the top with a thin layer of grass and sticks. Given a couple weeks, the upper layer would completely naturalize with the earth, making it impossible to see the trap.
The results would be simply disastrous for the enemy.
6- Use caltrops to disable cavalry
These are caltrops.
Prepare lots of these and give at least a couple dozen to each foot soldier and cavalryman in your army. Utilize them to disable fast cavalry attacks during the battle. Simply throw the caltrops in the way of the invading cavalry and many of them will never reach you at all. It will also slow down the approach of the remainders, as they will have to watch out for these deadly spikes.
There are many, many more methods you can deploy, but I thought these would be the easiest and most potent ones. The medic improvement and steam powered catapults (which I don't think can be built during a 6 months time) have already been mentioned by other users, so I do not need to reiterate any of those.