There have been many attempts in Christianity to draw a catholic (catholic literally means "universal") set of rules or principles on how the Bible must be interpreted. This is called the field of biblical hermeneutics (and there is an entire Stack Exchange devoted to this field/art). Hermeneutics is not exclusive to scripture, it is also applied to other texts. The goal of hermeneutics is to determine the objective meaning of the text, which may include attempts to understand authorial intent, historical/cultural context, and the grammatical and linguistic meaning of the words and phrases themselves. Many church councils were centered on disputes on how various texts should be interpreted, and creeds were developed to clarify the Church's position on various issues.
The field of hermeneutics has been applied to the Old and New Testament by both Jews and Christians throughout history. Early Jewish hermeneutics include the seven rules of Hillel which were passed down orally before being transcribed shortly before the birth of Christ, and Rabbi Ishmael's Baraita (13 rules) from the late first or early second century.
Seven ecumenical councils occurred throughout church history where specific interpretations of scripture were rejected or accepted. The goal of these councils was Church unity, thus it could be said that hermeneutics were being formulated through these decisions. I only reference seven because these were considered to be ecumenical and thus the decisions made at these councils are generally accepted by most major Roman Catholic, Eastern Orthodox, and Protestant traditions today.
- Nicea I (325) - The first part of the Nicene Creed was formulated which defined the divinity of the Son of God, refuting Arius.
- Constantinople I (381) - The second part of the Nicene Creed was formulated which defined the divinity of the Holy Spirit and refuted Apollinarism. The creed is sometimes called the Niceno-Constantinopolitan Creed because it was formulated in councils in both Nicea and Constantinople.
- Ephesus (431) - Christ was defined as the Incarnate Word of God, refuting Nestorianism; and Mary was affirmed as Theotokos (God-bearer). The Nicene Creed was declared as being authoritative and it became unlawful to hold to a different faith than that as defined by the creed (the creed defined the one, holy, catholic, and apostolic faith).
- Chalcedon (451) - Christ was defined as perfect God and perfect man in one person (Hypostatic Union), refuting Eutyches and monophysitism. Those who rejected the decisions of this council include the present-day 'Oriental Orthodox,' which includes the Coptic Church, Armenian Orthodox Church, and the Syrian Orthodox Church.
- Constantinople II (553) - The Church reaffirmed the doctrines of the Trinity and of Christ, further refuting Nestorianism.
- Constantinople III (680) - The Church affirmed the true humanity of Jesus by insisting upon the reality of His human will and action, refuting monothelitism.
- Nicea II (787) - The Church affirmed the propriety of icons as genuine expressions of the Christian faith, restoring the veneration of icons and ending the first iconoclasm.
From then on, the Church interpreted the scriptures in light of these councils' decisions, notably the one, holy, catholic, and apostolic faith as defined in the Nicene Creed. Various factions within Christianity have accepted or rejected additional councils and decisions, which further affects how they interpret scripture. It should also be noted that many modern Christian leaders do not consider any church councils to be infallible, to include the first Church council held in Jerusalem which is recorded in Acts 15. I bring all of this up because everyone interprets scripture in light of Church history and their historical and cultural context. Some groups insist that their sole authority is "scripture alone," but even these groups hold specific interpretations that have come about due to historical events. This is true whether or not these groups are aware of their biases. Clearly the Church has attempted to come to universal agreement on biblical interpretation, but numerous schisms and divisions have made this virtually impossible.
Prior to the Enlightenment, most Christians treated the bible as a special class of literature (sacred revelation), and thus did not apply textual criticism methods to its study. But during the Enlightenment it became common to read the bible as any other piece of literature, and historical-critical methods of interpretation began to be employed.
In general (painting with a broad brush), most conservative Christian groups now employ some form of historical-grammatical interpretation, while most liberal groups employ historical-critical methods. Another recent trend is trajectory hermeneutics, which asserts that since revelation is progressive, there is a "redemptive movement" or interpretive trajectory to the text that must be determined.
General Hermeneutical Principles
I will now attempt to answer the second part of your question: "is it possible to present such rules here in general?" I would not go so far as to call these rules, but they are general hermeneutical principles that guide most Christians today as they seek to understand and apply the scriptures.
- The original text (and the best text) must be used for interpretation.
- There can be but one sense of a Biblical word or sentence (i.e., the plain grammatical sense). Thus no interpretation is correct unless it is grammatically correct, that is, according to the grammar and syntax of the language in which it was originally written.
- The meaning of any phrase or word must be sought in its own context.
- Jesus Christ is the center of all scripture.
From this point on various Christian groups differ significantly (and some may not even accept those listed above, although most would). Most conservative Protestants assert that "Scripture interprets scripture," while Roman Catholics would include the authority of the Church and the Pope as having the ultimate right to interpret scripture. Many others have specific principles to avoid the misinterpretation of specific genres of literature within the bible (allegorical, prose, apocalyptic, poetry, etc.), although these principles are not technically restricted to biblical interpretation.
I tried to give a thorough answer that steers clear of taking the sole view of any specific branch of Christianity. For additional hermeneutical principles specific to your Christian tradition, I would recommend speaking to your priest/pastor and/or taking a course in biblical studies.