Martial is only an adjective, and it is narrowly defined. It describes things that are (1) of or related to war, (2) related to the armed forces, and (3) characteristic of or befitting a warrior.
Marshal (with one l) is broader. It can serve as a noun referring to (1) a person holding one of various official positions, (2) a military officer, (3) an officer of the law or fire department in the U.S., or (4) a person in charge of a parade or ceremony; or as a verb meaning (1) to arrange or place (usually military personnel) in line for a parade or maneuver, (2) to arrange in methodical order, or (3) to enlist, gather, or organize.
The words are easily confused. In addition to being homophones, they both also come up in the military sphere. The key to keeping them separate is to remember that martial is only an adjective, while marshal is never an adjective. It might help to remember martial in its two most common uses, in the phrases martial law and martial arts. Martial here is an adjective, modifying the nouns law and arts.
Marshall, with two l’s, is only a name.
Marshaled/marshaling vs. marshalled/marshalling
Outside the U.S., marshal is inflected with two l’s, to make marshalled and marshalling. These are the traditional forms.
In the U.S., marshal is now inflected marshaled and marshaling—with one l. In this it follows many other l-ending verbs that are inflected with a single l in the U.S.. Cancel and travel, for instance, make canceled/canceling and traveled/traveling. Different verbs have undergone the change from two-l forms to one-l forms at different times. In the case of marshal, the one-l forms started appearing in the late 19th century, picked up steam around the second world war, and finally became the more common inflections around 1990. The two-l forms still appear somewhat often, though—about once for every ten instances of the one-l forms in U.S. news stories from the last year.
The army also vows to terminate the martial law in force since the murder of former President Anwar Saddat in 1981. [Novinite.com]
The experienced mixed martial artist took over as soon as the fight hit the mat. [USA Today]
The women argue that too few offences lead to court martial, and hope their case will draw attention to the issue. [BBC News]
The Durham police and fire departments are looking for a man posing as a city fire marshal. [Durham Herald Sun]
Ferguson marshalled all his resources, dug in deeply, and the club and Glazers have emerged the other side. [Guardian]
Building such a tiny flying robot required marshaling an enormous amount of ingenuity. [Los Angeles Times]