SELECT

StandingOrderLine.OrderNumber,

StandingOrderLine.LineNumber,

StandingOrderHeader.OrderTotal,

StandingOrderPayment.PaymentAmount

FROM dbo.StandingOrderLine INNER JOIN dbo.StandingOrderHeader

ON StandingOrderLine.CompanyID = StandingOrderHeader.CompanyID

AND StandingOrderLine.StandingOrderID = StandingOrderHeader.StandingOrderID

INNER JOIN StandingOrderPayment

ON StandingOrderHeader.CompanyID = StandingOrderPayment.CompanyID

AND StandingOrderHeader.StandingOrderID = StandingOrderPayment.StandingOrderID

WHERE StandingOrderLine.LineStatus = 'Shipped'

There, fixed that for you. Perfectly readable. The owner or schema names don't need to be repeated in the On clause or the Select column list since they are specified in the Join clause, and some line breaks help.

As for the Where clause, just like you did here, I always repeat the table name on purpose in the Where clause, even if it's a unique column name across the tables in the query, to help future programmers who might be looking at my code and not be completely familar with the tables. You could say "Where LineStatus = 'Shipped'" but I don't do that.