Adding a new column should be simple. In most databases, it comes down to an ALTER TABLE statement. The challenge is doing it without locking tables too long, losing data, or breaking production code. Schema changes are one of the most common operations, and also one of the easiest to mishandle under load.
A new column changes the shape of your data. Every row gets the new field. On large datasets, this can be slow. Some engines rewrite the whole table during the operation. Others apply metadata-only changes. Postgres stores the column definition and fills it with a default only when read, unless you specify a non-null default that needs backfilling. MySQL may copy the table in some cases, depending on the storage engine and the exact change.
Plan for zero-downtime when adding a new column. That means understanding how your database engine handles ALTER TABLE. For large tables, consider an online schema change tool, like gh-ost or pt-online-schema-change for MySQL, or pg_rewrite scripts for Postgres. These approaches create the new column without blocking reads or writes for more than a fraction of a second.