On any connection (as a GdaConnection object), if the database provider used by the connection supports it, transactions may be started, committed or rolledback, or savepoints added, removed or rolledback. These operations can be performed using Libgda's API (such as gda_connection_begin_transaction()), or directly using some SQL on the connection (usually a "BEGIN;" command).
The transaction status of any connection can be obtained using gda_connection_get_transaction_status (), which returns a GdaTransactionStatus's object which can be interrogated. That object also makes it easy to keep up with the evolution of the transaction status of the connection.