I could write many pages about how fellowship is so incredibly necessary to one's faith. Based on my own experiences, the absence of fellowship with people of God can actually cause a person to completely abandon his or her faith, over time, even if the person is well-grounded in their faith to begin with. Unfortunately, people do not get proper fellowship from modern "auditorium churches" or "institutional churches", where a stage, podium, and microphone deliberately and intentionally drown out any activity of the body for immediate and active participation as body parts. As a result, fellowshipping in the home is now recognized by its proponents and its participants alike as the ideal, and biblical, approach for believers in Jesus to maintain fellowship.
There have been quite a number of different strategies and tools presented over the several years about how to organize house fellowship, among them ranging in semantics from "organic church" to "simple church" to "house church", and so on.
The way I am currently envisioning strategizing house fellowship guidance going forward is as such:
1) The simplest form of fellowship is with simply meeting with someone. Doing this even once with even just one other person, whether at their house or at the coffee shop or at McDonalds, is a demonstration of Matthew 18:20. You only need to make sure that you really, truly are meeting not as Christians but in the name of Jesus--that is, you are meeting in the authority and under the auspices of the kingdom, not to "hang out cleanly" but to spend time as brethren for the purposes of recognizing and being a part of the kingdom. For example, this is not going bowling or beer tasting among Christians. This is discussing kingdom matters, discussing the Bible, worshipping God together, planning an outreach, praying for each other, interceding in prayer for someone else, or going out into the streets to preach to the lost. This at a minimum should happen regularly, for all believers.
2) The second simplest form of fellowship is with a "Bible study group". I actually rarely encourage this kind of fellowship; not that Bible study groups are wrong (I love the Bible!), we should all be reading the Bible and studying the Bible together in a group should be a good thing. The problem is that these meetings are often either pretentious and spoonfed in theological delivery by a canned delivery system, sometimes even by heretical sources that carefully pick individual verses here and there to compile an often heretical topical monologue, or else these meetings not having a full breadth of scope of activities lack the discipline to actually study the Bible properly and instead devolve into gossip and small talk. If a group Bible study can be done well, I would recommend it only as an add-on to other forms of fellowship. Otherwise, I would strongly recommend that an individual study the Bible alone after spending time in prayer. A great resource for learning how to study the Bible in private study is Living By The Book.
3) The third simplest form of fellowship is with a "house fellowship", this being a once or more per week routine meeting with other believers in a home where the believers can meet and mingle with Jesus, fulfilling Matthew 18:20 on a scheduled basis. It should consist of singing, prayer, Bible reading, discussion, and food, and if anyone is sick or oppressed by demons then there should be healing and/or deliverance. Ideally, there should be many house fellowship meetings among many different hosts throughout the week, and anyone fully committed to the body of Christ should be rotating in attendance or else hosting once between several of them throughout the week. House fellowships are, by design, intended to be "ad hoc" attendance for all participants, but of course the development of godly relationships and spiritual support should be encouraged. Everyone should interact with godly love, and anyone acting selfishly and not in line with scripture as devoted to the kingdom should be addressed, and if not corrected then removed from the group.
Progressing in expectations from house fellowship, there are two paths to fork out to: 4) house church, or 5) fellowship outpost.
4) "House church", as opposed to "house fellowship", demands a more stable approach to the fellowship. It is more suited for married couples and families seeking long-term/permanent relationships, as it seeks to minimize risk and unplanned visitors. All participants are asked and expected to commit to attend, as opposed to people coming and going, ad hoc. Leadership is expected to form out. Biblical instruction is expected in every meeting. Being a reliable, peaceful, God-loving "family" that progressively deepens a knowledge and love of God over years is the objective, rather than a chaotic emergency room for people scrambling to deal with various problems and deliverances. Attendees are actually vetted up front; no one just shows up unannounced. I admire this form of fellowship, but it leaves out many who are single and/or suffering growth pains, and I would defer people to John Fenn and his organization CWOWI for this path of fellowship. [CWOWI Video Series: House Church 101]
5) "Fellowship outpost" is described here. It is the more suitable option for single men, single women supporting women, or for families that are willing to risk great vulnerabilities to their home to support their community all week long, while also hosting house fellowships at least once a week. This is what I feel is missing most in the body of Christ, yet on the other hand I've seen people naturally taking on the same responsibility in their homes frequently, people coming and going every single day needing a prayer or asking for some kind of assistance or just needing a place to rest their head for a few hours.
If the institutional or auditorium church with its own facilities should attempt to fill in the gap and attempt to accomplish serving and supporting any sort of meaningful fellowship, I would strongly hope that it accomplish it through the "fellowship outpost" approach. In my own personal opinion, aside from the self-interests of such charitable organizations, the fellowship outpost is the only reasonable Biblical explanation for any institutional church facility and organization in the first place.
Bonus: The "Zoom meeting" form of various fellowships can be used along with any of these. Obviously, virtual meetings using video chat does not have the effectiveness and substance that a live, in-person meeting would have. But in times where all attendees are spread out geographically or are otherwise blockaded from meeting in person, this can be a good way to facilitate interaction with the Body as a backup plan. There are several online meeting tools, not just Zoom, but here are some, each with their own strengths and weaknesses: Zoom, Google Meet, Jitsi Meet, Skype, and others.
Is God speaking to you to host or start something? Whatever you end up doing, it should come naturally. If it isn't natural, try just finding existing fellowships where you can participate without originating anything. Get more experience being with God's people, without any expectations on any "special" individuals, and recognize that everyone who has the Holy Spirit and was baptized in Jesus is a priest with full privilege access to the throne of God. Otherwise, if you are already outspoken and are already used to organizing meetups, depending on your house situation it should be straightforward enough to start something up, diving into whatever you feel fits most naturally.