Well, gregorian chant may be in Latin, but chant in general is a form of song without standard meter or set rythm (and I’m not a chant expert, just a musician - I know for a fact there are other liturgists out there that have had formal training in chant and could better assist you). I know when I’m playing keys at Mass and our priest chants the liturgy of the Eucharist, I ocassionally roll out a chord for him within a predetermined key, then roll out others at various points that are in keeping with the key and the major chord progressions. Specifically in our case we use the Mass of Creation setting which uses a combination of chant and the more familiar polyphony. The chant just allows the preist the flexibility needed to use more or fewer words depending on the celebration.
Essentially, when you chant by yourself you hit a pitch and stay on that for a few words, then you might change pitch a few different times as the spirit moves. If, for the sake of trying to line your chant up to some of the more traditional forms, you may do well to apply some of the more typical medieval modalities - if you were both musically inclined and have the desire and time to do the research. Research the music written in say 1000-1500 and get an idea for how some of the keys and scales worked and try to work within those.
If my memory serves me correctly - our Eastern Orthodox brethern have something like 8 set “tones”, each one varying to evoke a certain mood. I think they’ll do something like starting by having the priest or perhaps even the lector hmm the dominant note in the tone. Then start chanting a reading or part of the liturgy within the context of that mode, all concentrating on that first original tone.
So in short, if you’re by yourself, just try to “sing” what you say by staying on one or two notes - changing as the spirit leads. There may be a formal way of doing this, and if there is then by all means go with that method. If you really want to get a handle for some serious chant, start doing some research on Roman chant from the middle ages as well as some Eastern forms of chant (I think the Greek Orthodox folks developed the Eastern modes so that’s a good place to start).