Tables with no common columns

For a relationship to be useful, there has to be something in common between the tables, even if there isn't an existing pair of columns that you can match up.

For example, if you have a date table that only has a single column Date and a fact table that has columns for Year and Month but no Date column, you can construct a representative Date column on the fact table like this

Date = DATE ( Table1[Year], Table1[Month], 1 )

and then use this column for the relationship with the date table.

There are lots of other ways your tables might have granularity mismatches or need a bit of extra work in order to create a relationship. However, if there aren't columns on both tables that have some sort of logical relationship, then there's no reason to create a relationship between the tables at all.