This is the part I understand, what I'm not entirely sure about is how the floating leg of the swap is accounted for?

The issuer of a callable bond makes periodic fixed interest payments and (after a typical lockout period) has the right to call the bond on interest payment dates according to a fixed price schedule. The call price typically starts above par and declines toward par over time. The swap equivalent would be: 1) paying fixed in a interest rate swap and 2) owning a right-to receive fixed swaption. Bermudan swaptions are typically used to do this with the exercise schedule corresponding to the bond interest payment dates.To see why this works, consider what happens if interest rates fall sufficiently. The callable bond issuer can exercise their call, buy back the bond issue at a fixed price and reissue new bonds at a lower interest rate. In the swap product analogy, if interest rates fall sufficiently, the fixed payer can exercise the swaption (effectively cancelling out the original pay fixed swap) and pay ficed in a new swap at a lower rate.One thing that callable bond issuers can do using swaptions is to "monetize" the embedded call in callable bonds by selling offsetting swaptions. This generates funds but. by definition, puts the exercise decision of the callable bond into the hands of the party who buys the swaption. Note that there is a basis risk in such a strategy because the bond issuer's spread will generally not be the same as the swap spread.