The construction of Inter-Slavic languages has a long history. The first successful project was the so-called Old Church Slavonic, or OCS for short, which was introduced as the official language of both the church and state administration in early 9th-century Bulgaria, where production of books in the newly established Slavonic alphabets (Glagolitic, and to a larger extent Cyrillic) got generously sponsored by the central government for the whole existence of the country in Medieval times, up until its fall under Ottoman rule.
Around that point in time, the Russian Empire was emerging as a serious power in Europe and the introduction of a literary language was growing in importance there, so OCS was of paramount importance for the development of Modern Russian. It also had similar effects to other contemporary Slavic languages to varying degrees, depending on how important it had been in the centuries before their standardisation.
Generally, the Russian redaction of Old Church Slavonic is simply known as Church Slavonic and has been used in many Slavic and, mostly previously, some non-Slavic Christian churches ever since. However, nowadays most people find it too hard for actual day-to-day usage besides religious purposes. There are many reasons for this, but the main one is that all Slavic languages have simply evolved independently and in different ways. That is why there have been a lot of attempts for a newly synthesised Slavic lingua franca. Nevertheless, there are basically just two relatively serious projects that have remained promising lately.
Slovio is supposed to be easier for learning, even for non-Slavic speakers, while there is also Interslavic (medžuslovjanski / меджусловјански), which resulted after the merger of a number of other such projects and is closer to the actual living languages and thus claims to be easier to understand for any speaker of a Slavic language. Its grammar seems a little bit harder, though. On the other hand, Slovio’s motto apparently is “simple is better”, so maybe it would be better if you want a start with any real-world Slavic language.
I haven’t really learned or given serious attention for a longer period of time to any of the two, but as a Bulgarian speaker with a passive knowledge of a few other Slavic languages, it seems pretty straight-forward to understand both. For sure, I would say that any other such projects are not even worth considering anymore after the establishment of Interslavic. Unfortunately, the adherents of these two don’t seem to be agreeing on their philosophies. As far as I know, this is a common problem with many constructed languages, or conlangs for short, so I don’t see them merging anytime soon.
If you want more information, visit their official websites (slovio.com and medzuslovjanski.com, respectively). Then follow every hyperlink you encounter, or search for them in your favourite search engine. Please also consider studying actual Slavic languages, even only for passive usage (reading + listening).
Welcome to and have fun in the Slavic world! :)