There are many variations on monogamy and non-monogamy and each relationship is different. The most important parts are being true to your yourself, communication and trust.
Monogamy and non-monogamy are independent of sexual orientation and gender identity.
NOTE: I see labels as a rallying point to find people like yourself, not as a box to limit you. Positive uses for labels include exploring ideas and themes around your identity, knowing what words to google and finding people to talk to.
Monogamy is a form of relationship in which an individual has only one partner. Some people consider this to be one partner for life, others consider any number of partners monogamy as long as one relationship finishes before the next begins ("Serial monogamy").
Like so many terms, monogamy has a spectrum of definitions and definitions.
Polyamory is the practice of, or desire for, intimate relationships where individuals may have more than one partner, with the knowledge and consent of all partners.
It has been described as "consensual, ethical, and responsible non-monogamy".
Polyfidelity is a flavour of polyamory where the group of people is closed, i.e. there are more than two people in a relationship but the people are agreed on and not easily changeable.
Where one person, usually living alone, dates multiple others in a polyamorous way.
Swinging is about casual sex, although there can be a lot of overlap with polyamory especially as emotions are hard to separate from sexuality.
The Ethical Slut, by Dossie Easton and Catherine Liszt
"At last... a comprehensive, no-holds-barred guide for anyone who dreams of having all the sex and love and friendship they want. Here are the skills you need for successful - and ethical - sluthood, from scheduling dates to handling jealousy, finding partners to resolving conflict, raising children to caring for your health. If you've ever envisioned a universe beyond traditional lifetime monogamy, this is the book for you!"
Opening Up: Creating and Sustaining Open Relationships, by Tristan Taormino
"Drawing on in-depth interviews with over a hundred women and men, Opening Up explores the real-life benefits and challenges of all styles of open relationships — from partnered non-monogamy to solo polyamory. With her refreshingly down-to-earth style and sharp wit, Taormino offers solutions for making an open relationship work, including tips on dealing with jealousy, negotiating boundaries, finding community, parenting and time management."