Cool. A'right, I'm actually interested about that stuff in which a person connects with his guardian angel or an archangel stuff, I mean how/what method do they use for that? And since you kinda know about the Catholic faith, having a Catholic on your parents, how different would that be in praying to once angel?
Well this is going to end up being a long post. Sorry for that.
To answer this first part, depending on what variety of belief a person has in the New Age umbrella, these beings could be considered guardian angels,
spirit guides,
higher selves, or other things. The word 'angel' tends to be used in New Age varieties that have ties with Christianity (
Unity Church, for example), whereas varieties that have less to do with Christianity seem more likely to use the phrase 'spirit guide' or 'higher self' (which are not quite identical concepts, but called upon for essentially identical reasons).
This is where it's useful to mention some of the roots for where the umbrella of New Age beliefs comes from.
As a first root, there is
Shamanism and
Spiritualism. Shamanism is basically the world's oldest known form of spiritual practice, dating back to paleolithic periods. In Shamanism, a tribal shaman is thought to have the ability to contact spirits and/or ancestors, as well as do things like spiritual healing. Spiritualism is the more modern practice (from the 1800s and 1900s in Europe, and continuing today in New Age varieties) where mediums contact spirits or deceased people.
As a second root, there are philosophies like
Idealism and
Transcendentalism, which are related. These roots require a lot of explanation (hence all these links), but the short idea is that consciousness is the ground of all being, and your consciousness shapes your perception of the world rather than the other way around. This Idealist/Transcendental root builds some of the metaphysical architecture that is rather common in various New Age varieties.
A third root consists of Dharmic religious concepts (specifically the Upanishads and the Bhagavad Gita in particular, which were influential on American Transcendentalism and contribute ideas of reincarnation/rebirth as well as certain forms of
panentheism into the mix of New Age beliefs).
A fourth root consists of Abrahamic religious concepts, particularly Christianity. A lot of Americans and Europeans have Christian influence in their culture, so some of these beliefs are strongly tied into Christianity as part of syncretism or to make them more comfortable or to use as examples. Jesus, for example, is often put forth as an individual that mastered timeless metaphysical techniques like the law of attraction or a mastery of transcendentalism/idealism, rather than being a uniquely divine individual. The main contribution of Abrahamic religious concepts to New Age beliefs are symbolic- examples of Jesus and concepts like angels are a distinctly Abrahamic contribution.
Other roots often try to draw from science, other religions, technology, UFOs, various cultural practices, etc. Different subsets of 'New Age' beliefs, which may or may not identify as such, will generally focus more heavily on certain roots than others.
....
After all of that, a short answer to your guardian angel question in some New Age beliefs is essentially that you can contact a being for help simply by asking for it, much like any prayer. They're always there, according to the belief. Various groups of New Agers may have specific methods or rituals to do so, and if you have interest in that area you can seek out specific information on search engines, but essentially, a common idea is that you have all the power anyway. Much like how praying to gods, angels, or saints in other religions won't generally lead to a literal 'answer' but rather it's expected that the being is helping or sending 'signs', the response you'll get from a New Age perspective from one of these beings is the same. Signs, help, etc.
Other methods are things like:
-Seeking out mediums. Some of them claim to be able to contact the dead. The basic idea here is that you and they have the same power, but they're gifted at it. Like a pro athlete compared to you at a sport; you can both do it, but they're more practiced and talented at it. Some claim to be able to contact spirit guides, angels, higher selves, etc. The general situation here is that a person pays them money because this is what they do for a living, and the person uses their talents to contact a spirit directly and then offer guidance to you based on what the spirit guide says. Some people find this helpful, but from an an analytical view, especially with money involved, this would trigger a lot of empiricism/skepticism. The roots go all the way back to Shamanism.
-Use church programs or courses. My mother does this. Compared to the mediums, this option is generally free or less expensive, but also less direct and more group oriented. Some people belong to spiritual groups like churches that are essentially New Age, or
New Thought, or other varieties, and they teach people how to do certain things like create miracles or contact spirit guides. My mother does group phone calls where they learn about contacting angels, and also takes classes on learning law of attraction techniques.
-Using the
law of attraction. The idea here is that, as a part of the Divine, all of the power that you believe you're getting from external sources is essentially coming from yourself. You tap into your higher self to actualize your desired outcomes, with the principle example being someone like Jesus who was thought to heal on the spot due to his power. Since it's a syncretic set of religious beliefs, examples like the Buddha or Hindu gurus or other examples are often given. In other words, rather than asking for a certain outcome, you'd assert to yourself and the universe that a certain outcome is going to happen (or similarly, you thank the universe for already delivering it to you), because the idea is that you create what you think. The idea here is that whether you know it or not, you're always creating your own reality. The ideal situation is to raise your consciousness, realize that you're creating your own reality, and then take conscious control of it rather than allow to to act subconsciously or to come from your higher self without your direct awareness. This comes strongly from the aforementioned Idealist/Transcendental roots, and is an area of focus on the New Thought subset of beliefs.
....
There are some similarities and differences between a Catholic angel or saint, and a New Age angel, spirit guide, or higher self.
-As a similarity, these beings from both religions are called on to help. In Catholicism they can be understood as external beings that can help you. In New Age, they can be loosely understood as external beings, but really they're just part of a panentheistic framework where all is one.
-As a difference, Christianity generally frowns upon the idea of divination in general. Catholicism generally doesn't provide a framework to literally contact an angel and get an answer, but it's thought that prayer to angels and saints can help. In New Age, with mediums or other methods, it's thought that in some cases, these spiritual guides or angels can give literal answers.
-As another difference, in New Age beliefs, there is often a belief in panentheism or monism; the belief that all is one. Rather than calling on a truly separate being (like how in Catholicism there is a separate transcendent god, and then separate souls, which are not called "one"), you're calling on an aspect of yourself, which at your level for practical purposes, is viewed as another being. In panentheism, there really is only one being here, at the highest level of understanding.
As you all might probably know, I'm a Catholic Christian, though most sects don't really recognize it as Christian 
