Depends on the person. Generally I find, it goes one of three ways.
If you are both doing everything equally you have a joint account and alternate coding days. You come up with the story line together and then when it’s the next persons turn you tell them what you have done, then they elaborate. Sometimes you come up with exactly what needs to be coded together and then take turns coding.
Another way is split jobs. Sometimes you will have someone designated to creating the plot, plot ideas, turning points, etc. and the other is based on coding.
The other way is by google docs. Sometimes people prefer to make a google doc that they write a brief script concerning animations used and dialogue spoken, then you take turns writing it (or sometimes one designated person) into an actual episode with spot directing, overlays, cuts, zooms , etc.
Usually when writing with a partner you have a joint partner account.
These are just a few ways writing with partners is done.