the bad news is...
Treaty Law Research is NOT intuitive
the good news is...
there are useful guides out there to help you find free and subscription-based treaty databases
The Vanderbilt Law Library has a Treaty Research Guide online
The ASIL Public international Law Guide contains a section on treaty research
Globalex also has a guide on Treaty Research
Full Text Treaties
Even though you can find treaties using these sources:
the most comprehensive collections are
an almost comprehensive collection of treaties
secondary sources to help you understand the treaties