If you are a foreign-born person in the U.S. whom the immigration enforcement authorities are placing in removal proceedings, you will receive what's called a Notice to Appear (NTA). The NTA will specify the date and place of your initial removal hearing in immigration court. You will be expected to personally attend this calendaring hearing and (assuming you ask for one), a later individual, merits hearing. This is true even if your lawyer (or another representative) attends as well.
Try your best to go to your court hearing as scheduled. Nevertheless, if you are unable to attend, you can request that the date be changed. The procedure for this is to file legal paperwork called a motion for a continuance. The Immigration Judge (IJ) has wide discretion to grant or deny such a motion, and you take additional risks by rescheduling a hearing.
(We are assuming that the reason you can't attend has to do with scheduling, not location. If, however, you have moved to a different part of the U.S., it might be possible to ask for what's called a change of venue.)
You will most likely want to get a lawyer's help with this (as with the rest of the removal proceedings). The attorney will be familiar with the procedures in the Immigration Court Practice Manual, which must be closely followed.
IJs decide motions for continuance based on the unique facts of each case. You (or more likely your lawyer) must submit a written motion, explaining in detail why you need to reschedule the hearing.
It is helpful to attach supporting documents explaining why you have "good cause" to ask for a continuance—such as a medical note from your doctor saying that you are scheduled for an urgent procedure. You are more likely to be granted a continuance if you can demonstrate that you (or your immediate family members) would face some great hardship if you had to attend the hearing as scheduled.
For example, if you (or your immediate family member) must undergo surgery on the day of the scheduled hearing, you are likely to be granted a reschedule. On the other hand, simply being scheduled to go to work on the day of your hearing is not likely to be enough to obtain a continuance.
Also, IJs are more likely to grant your request if this is the first time you are asking to reschedule.
File the motion for a continuance as soon as possible before your scheduled hearing date. In your motion, feel free to suggest some reschedule dates you would prefer. The IJ, of course, has discretion to choose any date to reschedule your hearing to.
Make sure to follow all procedures, deadlines, and filing requirements of your specific IJ, and to serve (send a copy of) your motion for continuance on the government trial attorney, as well.
You must attend your removal hearing if your motion for continuance is still pending (undecided) when that date arrives. In other words, unless you receive an order granting your motion for continuance, you must personally attend your removal hearing as scheduled. If you do not, the IJ can determine the outcome of your case in absentia (without your presence at the hearing).
Because you are unable to present your case during a hearing held in absentia, the IJ is likely to order you removed. Such an order cannot be appealed, unlike orders entered after a hearing in which you do appear. (You can file a motion to reopen such a decision, but those are very difficult to win.)
Make sure to arrive at your hearing on time. Plan ahead, and give yourself adequate time to find parking and to go through the security screening. If you are late to your removal hearing, the IJ may order you removed in absentia, too.
If your rescheduling request is granted, you will receive an order granting your motion to continue. Typically, rescheduled hearing dates are set within a month or so after the original hearing date. However, IJs are very busy, and might not set a reschedule date until many months after the original hearing date.
If you reschedule your asylum hearing, the clock will stop on your work permit eligibility until the rescheduled hearing date. That is, the 150-day period (counted from the date when you filed your asylum application) that must pass before you are eligible to apply for a work permit will be delayed. For more information, see When Can Asylum Applicants Get a Work Permit?.