this is how standard transformer can be wired as auto transformer with some numerical examples.
as others have pointed out, for electrical circuit to work, there must be a closed path. only then current has a way to go. so both input and output side will need two wires. connecting single wire to a primary is an open circuit

 

you also need to size transformer correctly. you need one with secondary that has suitable output voltage AND output current.

for example you live in a place where you expect 120V but your outlet only measures 104V. the difference is 16V but since transformer is made for 120V primary, and not 104V, using transformer with 16V secondary would get you less than 16V that you want.

in fact you will get 16V * (104/120) = 13.87V.
not a big deal but if you want to be exact, you would try to choose transformer that has a bit higher voltage on the secondary:
16V*(120/104)= 18.46V

so you can pick 18V or 19V variant...

say it is 18V. the ratio 120V/18V = 6.667
but sine mains voltage is lower and only 104V, output you get will be 104V/6.66/ = 15.6V which is very close to correction value we aimed for (16V).

next you need to consider load current. assuming you want to power something that draws 5A, you would want your transformer secondary to also handle 5A (or more).

120V * 5A = 600W (load)

but the transformer is only 18V*5A = 90W so you can pick 100W or larger.

reason that transformer is smaller than the load is because transformer does not provide all power to the load, only the difference to correct low mains voltage.