Quick note: studying and meditating on your own is okay, to a point. Before you convert, it is important to study under a respected member of that faith for multiple reasons:
1) You want to be accurate. While traditions vary between cultures, religions like Buddhism, Hinduism, various classical forms of paganism and tribal religions, and Zoroastrianism have become quite popular in the West for their exotic nature. Sometimes it leads to sincere scholarship and devotion. But more often than not it leads to what we in the religious studies field call "White Shamanism".
People accidently or intentionally cherry pick a faith or get a superficial understanding from self-fulfilling or poor resources and then butcher the faith. The popularity of adapting Native American practices half-assed is what gave the name to this phenomena. It's cultural approperiation at it's worst.
2) You need a support group. Community is key in religion. Community helps the convert learn the path and sustain it as well as provides refreshing life and rejuvination to the part of the community that was born into it or has held their beliefs for a long time.
3) You need to know the context of things. For example with Hinduism, some things are strict from the Vedas. But other "Hindu" customs, relics, or holidays aren't actually Hindu at all, but are Punjabi or any other ethnic group and have been falsely attributed to Hinduism. Careful study is needed to make sure you are understanding the faith, and not accidently taking in things that don't apply to you as a convert. Understanding how things have evolved or adapted also helps keep you grounded in your faith. It also shows respect to the cultural groups that accept that faith from birth and builds credibility for yourself.
And all this builds to the ultimate challenge:
4) You need to be confident and secure in your reasons for conversion.
Do not convert because something looks cool, someone you love is there, or it possibly fills an immediate need. It's perfectly natural and healthy to have an initial curiousity and fascination with the new and novel. But religion isn't supposed to be a club, it's an ethos intended for the practicionar to filter their life through in order to achieve something fulfilling.
This shouldn't be done quickly or rashly. Curiousity is a good start, but conversion should only occur after contemplative study, respected consultation and guidence, and deep meditation. You will know if it's right by how you feel inside and a inner confirmation that is hard to articulate. Even if you are struck with initial awe, your newfound faith can only be enriched by paitent study and self discovery, never hurt by it. So no hurry.
After I left my birth faith, I just kept my heart open. I am a religious scholar so I studied many faiths, but when I began to study what I would eventually convert to, something seemed just, fulfilling on more than just an academic level. I made a mental note and proceeded onward, but it just kept tugging at me. I ended up following all the steps I mentioned above, even taking the intensely nerdy route of learning to translate the faith's text (which is great but not required a lot) for myself. And that pull grew to a personal fulfillment, not just an academic one. So I followed it.