How to join two lines in QGIS

Let's assume that you want to join 2 lines in QGIS:

Activate edition mode and click on the magnet tool:

Click on the first vertex and bring the cursor close to the second one:

At this point, you'll have a continuous line. Finally, dissolve attributes of both lines to have only one entry on the attribute table. Go to:

Vector > Geoprocessing tools > Dissolve

Here is the final result: