Imagine yourself going through any kind of doorway, mirror, pond, cave, a hole in a tree, walking down a path, etc. Whatever you envision, just make sure you are going through something or making some transition. This will allow you to move from your mental imaginative space into the astral realms. When you reach the other side pause and take stock of your surroundings. Don’t force anything into existence, just take note of how things look, what kind of setting you’re in, what season it is, day or night, and what sounds you can hear. This will help you to solidify your presence there.
Note: If you don’t visualize well, don’t see anything or anything else that you feel might be “off”, it’s ok! Don’t worry about it, keep going with where you are currently. The next lesson covers this in detail!
You should always set an intention before you go, a journey without a purpose can be scary or it can be the most boring 20 minutes of your life. Your first intention should be to meet your familiar(s) (I work in a tradition where everyone has 3, a prey animal, a predator and a carrion animal but your mileage may vary). You familiar is a soul-double, you are literally sharing a soul with this being and they have created a separate consciousness to be able to guide you. Trust them. They will help keep you safe (though not necessarily all in one piece) and they'll help you navigate the astral. After your first journey, your intention is up to you. Explore, work on your personal needs, learn magic, ask your familiar for guidance, it’s up to you!
There are three main realms in which we journey: the lower world which holds all the possibilities for this world and which is also where we tend to meet familiars and other helping Spirits; the middle world which is the spiritual equivalent of the "real" world and ordinary reality, and which is where we deal with issues of relationship, past lives, and the like; and the upper world which is very symbolic, often suffused with bright light, and where we tend to meet spiritual beings such as deities, ascended masters, etc.
There are a multitude of realms contained within each of these subcategories but understanding the primary type of realm you're trying to reach will help greatly.
Keep in mind, while it can be uncomfortable, dismemberment is a powerful form of initiation. Many, many astral travelers that I’ve met had very visceral dismemberment journeys as their first. If it happens to you embrace it, you can't die over there and those experiences lead you into necessary and often amazing shadow work. These kinds of astral experiences are a kind of symbolic death and rebirth into a new state of being, one lived in two planes of existence!