Comment 1 for bug 1427401

A work around for creating a new record is as follows:
1.) Export the current database as a text file by doing the following:
    1.a.) File --> Export --> Database to SQL file
    1.b.) In the "save as" dialog choose location and file name using the ".txt" file extension to save the file as.
2.) Open the text file saved in step 1.b. above in a text editor and find the line where you would like to insert an record.
3.) Make sure the record being inserted has the same format as other records in the text file form of the database.
4.) After inserting your record (by typing it in) save the file and close it.
5.) Go back into sqlitebrowser and perform the following task:
    5.a.) File --> Import --> Database from SQL file
    5.b.) In the "open" dialog browse to the location where you saved the text file from step 4. above and open it here.
6.) A dialog will open asking if you wish to create a new database file to hold the imported data.
    6.a) Answer "Yes" and save the database in the same location as the current database with a different name.
    6.b.) If you answer "No" sqlitebrowser will crash.
    6.c.) If you answer "Yes" but attempt to save the database over the current database being used, you will get a dialog stating the following: "File /path/to/your/database/your_database.sqlite already esists. Please choose a different name" with the only option here being an "OK" button. Selecting this button takes you back to the sqlitebrowser where you will have to start over from step 5. above.
7.) Once you have completed step 6.a. above close sqlitebrowser and delete the record of the current database you were attempting to change.
8.) Rename the database saved in step 6.a. to the name of the database that was deleted in step 7.

Once step 8 is completed, you have now successfully added a new record to the database via export and import operations. You can open the newly renamed database in sqlitebrowser and if you've followed the above steps correctly you should have a new record located in the database exactly where you placed it in steps 2 through 4 above.

This post is currently the only solution for creating a new record until the "new record" button gets fixed as per the original post's bug report.