If a local field is being changed then you are still in browse mode when you should be in Find mode. Also, a global field will work better for what you want here.
Define a new global field, gFindCriteria. To define a global field, define it in Manage | Database | Fields and then click the options button or double click the field defintion to bring up field options. Click storage tab and choose the global storage option.
Now the script:
Show Custom Dialog ["Enter data..." ] //Specify Input field1 for gFindCriteria
Enter Find Mode
Set Field [YourTable::YourField ; YourTable::gFindCriteria ]
Set Error capture [on]
Perform Find 
This is very helpful! I have a script that has two parts. The first is similar to above where the user inputs a report number and the related records are shown. For the second step, I want to find related records that are < the report number the user input. Is there a way to do this? Thanks!