Before we start:
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Supported subtitle formats in Avid
Avid only supports two formats: .txt or .STL. In this demo, we use .txt file as an example. The content in an Avid compatible .txt file would be like this:

STEP ONE: Import subtitle file into Avid
Add a video track on top of your timeline and rename it as Subtitles (or whatever you prefer).
Go to your Project Window (or CMD+9) ----> Effect ----> Generator ---> SubCap.
Drag the SubCap Effect to your Subtitles track. You will see a clip named 'Filler' on this track. Make sure it is as long as your timeline goes.
Open Effect Editor Tool.
Click on 'Import Caption Data' Button.
Select 'Avid DS Caption File (*.txt)' in 'Files of type' dropdown menu.. (You can see there are only two file formats supported by Avid.) Select your .txt subtitle file in browsing window and click Open.
If the timecode in your .txt file matches with your timeline timecode. Now your subtitles shall fall on your Subtitles track as individual clip.
STEP TWO: Adjust subtitles in Effect Editor
Open Effect Editor Window again. In order to apply a universal style to all of your subtitles, we need to Edit Global Properties first.
In 'Synchronize' tab, make sure you select "Track" for each item for now. This will enable you to standardize the font/size/position etc. for all of your subtitles. Click OK.
You can adjust the font/size/outline/shadow of your subtitles in 'Text Appearance' and 'Box Appearance' tabs. Here's a reference setting if you want to put your subtitles in the lower center of your image without a black box background.
1. Choose "Center Align" at the bottom of 'Text Appearance'.
2. Adjust the Opacity to zero in 'Box Appearance'.
3. Below that, choose 'Anchor To Bottom of Text' and 'Anchor Center' in 'Box Appearance'
4. Adjust 'Anchor Position' until you satisfy.
You can also turn on the safety line as your position references by clicking on 'Grid' button on right side of Effect Editor Window.
STEP THREE: Revise Subtitles Content
If you want to revise your subtitles, go to 'Edit Master Caption List' in Effect Editor Window.
Now you can type in your subtitles in 'Caption Text' boxes.