A dental crown is intended to protect the underlying tooth from further deterioration. It's a dental restoration, and as such, it restores the tooth to its former shape and strength, courtesy of the protective porcelain shell that now encases the tooth. It doesn't always work out that way. If a tooth beneath a dental crown experiences deterioration to the point that a root canal is necessary, how can you get a root canal with the physical obstruction of the crown?
A dentist will first investigate whether the crown can be removed without damaging it. This isn't as simple as it might sound, since the crown was securely bonded onto the underlying tooth—so securely, in fact, that un-bonding a crown while leaving it intact can be impossible. This depends on the age of the crown and the condition of the underlying tooth (as any deterioration may have reduced the strength of the bond). If possible, then your dentist will certainly remove the crown, retaining it so that it can be put back into position when the root canal has been performed.
Through the Crown
If removal is not possible, then your dentist may opt to perform the root canal through the crown. A root canal requires your dentist to make an access cavity in the tooth, in order to remove the infected or dead dental pulp from the tooth's internal pulp canal. This access cavity is usually created in a straight vertical line with molars (teeth with a flat biting surface), or on the rear section of teeth anterior teeth (such as incisors or canines). Using a drill or dental laser, your dentist will simply make the access cavity through the porcelain crown.
This access cavity created in a dental crown will render the crown useless for its intended purpose. The dental pulp will be removed, with the pulp chamber irrigated and sterilized, before the empty chamber is filled with a packing material (a latex known as gutta-percha). Clearly, the dental crown is no longer intact, however this is now less relevant, and it can be removed and discarded.
Filling and a New Crown
Root canals are typically given a provisional filling, which then settles. The final touch for a tooth with an extracted dental pulp is usually a dental crown, although the need for a crown can depend on the state of the tooth and the size and location of the access cavity. In your case (when the tooth already had a crown), a replacement crown is mandatory, and this will be fabricated while the provisional filling is settling, and will then be bonded to your tooth.
If a dental crown can be removed and reused during a root canal, then this will happen. If not, the dental crown won't prevent the root canal from happening, although a new crown will be necessary.