There are two primary types of challenges: opposed checks and difficulty checks. Opposed checks are involved whenever you are acting against an individual, whereas difficulty checks are generally reserved for inanimate objects. Both involving rolling skills, which is achieved by rolling a number of six-sided dice equal to your score in the skill. In the event that a character's score in a given skill is 0, 1d4 is instead rolled. In chat, this is achieved by typing Xd6 [skill name] (or 1d4 for a skill of 0), at which point the dice bot in the channel will automatically generate a result.
I. Opposed Rolls
Opposed rolls are used whenever you attempt to defeat another character's skill. Combat is resolved in this manner, as are other conflict-related abilities: the initiating player rolls their check and the defending player rolls their opposing check. The highest roll wins, with ties going to the defending player. If it is not immediately apparent which player is the defender in a given situation, a GM will make the ruling. For more details on combat, see the Combat article.
II. Difficulty Checks
Difficulty checks are not remarkably different from opposed rolls - one dice result is simply changed to a set number. You must achieve equal to or greater than the difficulty to succeed. These difficulties are not always available to the player, nor is the success or failure. It may be immediately apparent if, for example, one fails an Agility check to scale a wall. It may not, however, if one fails a Technologist check to disable a silent alarm. Something helpful to keep in mind.