how does one access the country's boundary relation?

Probably a more beginner-style answer is appropriate here ;)

So, how to access the Country-Relation:

1) Zoom to a part of the border

2) Choose Edit in Potlatch

3) Select a part of the border

4) Go to advanced mode

5) In the lower part, after the tags, you see, which relations have this way as a member. By double-clicking the relation number, the relation opens in a new window.

6) Repeat this, until you find the needed relation. Most country boundaries are members of several relations, as they are boundaries also of the neighbouring country and several lower admin levels like provinces, counties etc.

7) If you found "your" relation, you can choose the advanced mode in the relation view window, and look at the tags, edit them, or add new tags.

NOTE: Country boundaries can be an emotional topic. To avoid edit wars or hard feelings, check with the local community if you change something important, like the language of the main name-tag, for example.

A simple way to find any boundary is to launch www.osm.org and to navigate the map to that border.
Borderlines (ways) are violet dotted lines.
Once you see the borderline, expand the upper right icon on the map (layer stack), select Browse Map Data.
Better click Hide areas
With the hand, select the border and you see its tags on the left.
Click details and check that you've got what you want (that is a way, a borderline)
Click on the containing boundary relation you want at the bottom of the page
From there, depending if you're using subareas, you may be able to navigate up and down boundary levels.
Once found, click Edit Relation, JOSM recommended
Have fun

The boundary is a way-element just like a street is.

Find the boundary :)