Well, there's a number of ways to crash it, but assuming the hacker is doing it (and not a mage or spirit or street sam with a really big gun), here's how it goes.
1. Before anything, the hacker and the copter need to be in AND STAY IN Mutual Signal Range. Given that a Lone Star copter, straight out of the book, would be a security vehicle, the on-board node for it would have a Device Rating of 4 (meaning the Firewall / Response / Signal / System attributes would all be 4). Note, this assumption is one of the biggest things that causes this entire process to fail. For example, a copter that knows it's being hacked and doesn't need constant contact with HQ or drones could lower it's Signal rating voluntarily. But assuming it doesn't...
Mutual Signal Rating of 4 = 1 km (SR4A, pg. 222).
2. If the copter's node (which we'll just refer to a the copter from now on) is running in Active or Passive mode, then the hacker is automatically aware of it as soon as it is in Mutual Signal Range. If it is running in Hidden Mode, there will need to a Detect Hidden Node test. Which mode the copter is running in is largely dependent on what the copter was doing before it started chasing the runners. If it was patrolling, it was probably in Passive Mode. If it was explicitly dispatched to get the runners, it was probably in Hidden Mode. Changing the mode is so easy to do, however, that the only reason it wouldn't be in Hidden mode is if the copter was in Passive mode and was surprised by what the runners did and didn't think to change modes.
Detect Hidden Node Test: Electronic Warfare + Scan (4 or 15+, Complex Action, SR4A, pg. 230).
The difference in threshold is based on if the hacker knows where the copter is, i.e. can see it or otherwise detect it before trying to detect the hidden on-board node.
3. Assuming the party does not have the decryption key for the copter and that the copter is has Encrypt running (which is so inexpensive and common, it would be foolish not to), then the hacker needs to break through the Encryption on the copter. Now, this is another aspect that can foil hacking attempts. Since the desired goal is to crash the copter, one needs access to the node in the copter itself, not to one of the slaved devices (i.e. drones) that might be coming with the copter. According to the Strong Encryption rules in Unwired, it is possible to spend time (and nothing but time) to thoroughly encyrpt a node, making the time interval for each Initiate Cryptanalysis test equal to the time spent, to a maximum of 24 hours per test. Given that fights in Shadowrun usually take only seconds, waiting for the decryption can pretty much prevent in-combat hacking. But, assuming that the copter isn't using Strong Encryption...
Initiate Cryptanalysis Test: Electronic Warfare + Decrypt (2x Encrypt Program, 1 Combat Turn, SR4A, pg. 230). Once the Test is started, you do not need to spend actions continuing it. It runs by itself and you wait for it to finish. Note: This test does not benefit from any teamwork test.
Given that the Device Rating on a Lone Star copter is a 4, the (typical) maximum program rating running on it is also 4. So the threshold on this will probably be 8.
4. Once the encryption is broken, one needs actual access to the copter. This is a Hack-On-The-Fly test. Given that the copter is probably being piloted by an actual person (either on board or rigged), you will also need admin access to have a chance to boot them off to control copter, since a copter can only accept commands from one account at a time.
Hack-On-The-Fly Test: Hacking + Exploit (Target's Firewall +6 for admin access, 1 Complex Action, SR4A, pg. 235). Each time you make this test, the target node gets a Firewall + Analyze (Your Stealth Program). If successful, the Firewall increases by 4 and the node is considered 'on alert'. If you are successful, you automatically log on with the completion of the test.
Given, again, the Device Rating of 4, threshold for this test is likely 10 (4 + 6) and the copter gets a Dice Pool of 8 (Firewall 4 + Analyze 4) to beat your Stealth Program.
5. Assuming all of this is successful, and we talking about a minimum of 1 Combat Turn and 2 Complex Actions, then you are logged into copter as an admin and it is entirely possible that the pilot does not know that you are in his system. Depending on the situation, the pilot himself may only be logged into the copter as a security personnel, in which case, you can spend a Complex Action to terminate his connection, leaving you in control of the copter to do with as you wish. But in case they also have an admin account, then it becomes a matter of who can dump who first.
5a. Cybercombat Option: Chances are good that riggers do not have the programs loaded to defend themselves well in cybercombat. A few Complex Actions of Cybercombat + Attack versus a poor Cybercombat Defense and Soak and you might just off-line their system.
Cybercombat Test: Cybercombat + Attack Program / Blackout Program / Black Hammer Program vs. Response + Firewall (SR4A, pg. 236). Net hits add to Attack Program Rating for Matrix Soak
5b. Shift Mutual Signal Range: If the copter is remotely controlled or remotely rigged and you are closer to it than the original pilot, change the Signal Rating so you are in Mutual Signal Range and they aren't, but obviously doesn't work if the pilot is on-board.
Shift Mutual Signal Range Test: Electronic Warfare + Command (1, 1 Complex Action, SR4A pg. 229 as Control Device).
At this point, it is has been at least 2, if not 3 Combat Turns to hack into a copter and force it too crash. Assuming that the fight has lasted this long, you are either doing a very good job of keeping buildings and bridges between you and the copter or have a significant distance advantage. During that same amount of time, the mage in the party could have summoned a spirit with the Accident Power and sent it after the copter, using a dice of 2x Force vs. the 2x Intuition of the pilot to cause a Crash Test, or the gunners could have some luck in shooting it from the sky. And this is all assuming the security spider back at HQ didn't spend the 15 minutes necessary to turn that 1 Combat Turn time interval into a 15 minute time interval, in which case he will be getting fired for such a costly rookie mistake.
Honestly, hacking in combat really only happens if you are on the defense, protecting your teams assets from being hacked, or you have the decryption key and have spent time detecting the hidden node and hacking-on-the-fly as part of an ambush.