What is the best way to join following tables? I have 55 records in the second table and I would like to just "drag and drop" the data to the first one.
Shapefile table Database table
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As I mentioned in comments, no join is currently possible because there are no records in one table to join those from the other to.
The simplest, easiest, fastest thing to do is create your line features and enter a unique ID attribute for each record that is found in the table you already have. You can then join your table to the features using that ID field in both tables.
You mention wanting to just copy them over, click a row, and draw the line. ArcGIS doesn't work like that. To pursue this route you would have to:
Create new attribute fields in your shapefile that match the datatypes (and preferably field names, though you can map from one name to another) of your table.
use Append, Load Data, Copy Features, or a similar tool to get the table records loaded into the shapefile. Some of those tools may or may not like the lack of a geometry (shape) column and not successfully complete the operation. You can also copy the attributes from each record in the table, one at a time, and paste them to the last row in the shapefile table (there should be a blank row at the bottom when in an Edit Session). What you will end up with is records with a null geometry.
Selecting each record, you'll need to use the Replace Geometry tool on the Advanced Editing toolbar to create a new geometry to replace the null and then save edits.