The Standard Half-Cell and its Reactions
If the potential of a standard half-cell is assumed to be zero (0), then the experimentally measured difference in potential between the standard and a second half-cell is the relative potential of that second half-cell.
 
The standard half-cell assumed to be zero (0), is the H2 half-cell.  It is a half cell with H2 gas bubbled in at SATP over an inert platinum electrode.
The other type of cell is the Daniell cell.  It involves 2 separate beakers, each with a 1/2 of the cell.  The cells are connected by a physical U-tube filled with a salt solution.   Below is a standard cell with Ag and H2.
 
In any standard cell the electrolytic concentrations are always 1 M.  Below is a  H2 | Zn standard cell.
 
Ex  #1:    Zn | Zn+2 ||  Ag | Ag+1  Galvanic Cell

Go to the redox table and find both sets of equations:

Eo = +0.80 V    Ag+1(aq)  + e-1  --->  Ag(s)  reduction
Eo = -0.76 V    Zn+2(aq)  + 2e-1  ---> Zn(s)  oxidation
Zn has the weaker reduction potential therefore it will be oxidized. Reverse the direction of the arrow and the polarity of Eo of the Zn reaction.

Eo = +0.80 V                  Ag+1(aq)  + e-1  --->  Ag(s)     reduction
Eo = +0.76 V                  Zn(s)  ---> Zn+2(aq)  + 2e-1     oxidation
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Ecell = +1.56 V        2 Ag+1(aq) + Zn(s) ---- > 2Ag(s)  + Zn+2(aq)
 


 
Ex.#2  Ag | Ag+1 || Cu+2 | Cu
Eo = +0.80 V      Ag+1(aq)  + e-1 ---->  Ag(s)  reduction
Eo = +0.34 V      Cu+2  +  2 e-1  ----->Cu(s)   oxidation

Therefore
Eo = +0.80 V     2 Ag+1(aq)  + 2 e-1 ----> 2 Ag(s)  reduction
Eo = -0.34 V      Cu(s) ---->  Cu+2  +  2 e-1          oxidation
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Ecell = +0.54 V   Cu(s)  + 2 Ag+1(aq)  ---->   Cu+2(aq) +  2 Ag(s)
 

Ex #3:  What is the standard Eo potential for the reaction between  Ag | Ag+1 || Al+3 | Al ?

Eo = +0.80 V      Ag+1(aq)  + e-1  --->  Ag(s)    reduction
Eo = -1.66 V      Al+3(aq)  + 3 e-1  -----> Al(s)   oxidation

Therefore
Eo = +0.80 V      3 Ag+1(aq)  +  3 e-1  ------>  3 Ag(s)  reduction
Eo = +1.66 V     Al(s) ------>   Al+3(aq)  +  3 e-1          oxidation
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Ecell = + 3.46 V     Al(s)  +  3 Ag+1(aq)  ---->  Al+3(aq)   +   3 Ag(s)        

Go to the Standard Half-Cell Potentials Worksheet