There are many ways to edit Block Attributes. The standard method is to simply double-click the Attribute to invoke the Enhanced Attribute Editor.
Use the Attribute tab to change the value of an Attribute. Use the Text Options and Properties tabs to change: Text style, Justification, Height, Width Factor, Oblique Angle, Layer, Color, Lineweight, etc.
So how does one edit more than one Attribute at a time? You can select the Blocks and use the Properties palette to modify values of common Attributes. Consider the three insertions of the two Blocks shown here.
Both Blocks have an Attribute with a tag name SEC. When three of the insertions are selected, the common Attribute Tags are available to edit in the Properties palette. Change the value as desired.Global editing of Attribute values can still be accomplished with the old, tried and true, -ATTEDIT command. Don't forget the dash; ATTEDIT alone invokes the older (non-Enhanced) Attribute Editor dialog. The -ATTEDIT command exists virtually unchanged since the very early days of AutoCAD, so the syntax is a bit clunky, but it will allow you to replace all or part of an existing Attribute value on all or selected Blocks. -ATTEDIT will also edit other Attribute properties beside value, but one by one, not on a global basis.
There's also an Autodesk supplied Express Tool, GATTE, that globally changes the selected Attributes' value only.