An executor is the administrator of a will, appointed by the deceased. You may object to the appointment of a certain person as executor of a will, questioning whether the person who claims to have been appointed by the deceased actually was. This is called "contesting the executor." Or you may object to how the executor handles administration of the will. You can also challenge the executor on that count.
Check if the will, in which the executor likely is declared, has two signatures. If the will was filed with the probate court, it is a matter of public record and you will be able to read it there. If two people did sign it and the person claiming to be executor was designated in that will, it is unlikely that you will be able to successfully challenge the executor in the sense of the legitimacy of his appointment, unless you can produce a more recent document in which the deceased names a different executor.
Contest the executor by filing a challenge with the appropriate probate court (usually at the county level). Have an argument prepared as to why you believe the deceased did not mean for the current executor to serve as executor. This is a very difficult argument to win.
Challenge the executor's administration of the will by filing a challenge with the appropriate probate court, usually at the county level. Have an argument prepared as to how the executor has breached his/her fiduciary responsibility. You may want to familiarise yourself with the fiduciary responsibilities of an executor (for example, periodic filing and accounting) to know what transgressions could actually win your case.
Anyone with an interest in the decedent's estate can challenge the executor. You can also try to get the executor removed if she has been convicted of a felony. Other grounds would be a display of misconduct either directly or indirectly imperilling the estate (for example, theft from the estate or repeated drunkenness, respectively).
Keep in mind that there is a time limit for such challenges, so act with some urgency. The argument contesting the executor likely will have to be more substantial than "If s/he had known the lawyers would be so expensive s/he wouldn't have appointed one as executor." If the decedent was of sound mind when making the appointment, the court can't go against the decedent's wishes so easily.