Kick the carpet seams so that they stretch at least 1 inch past the joining point. Carpets will shift over time, and you need enough extra carpet overlap so that the seams don't stretch and split.
Lay a strip of hot melt adhesive underneath where the carpet will be joined.
Plug in the heat seaming iron and allow it to heat to full temperature.
Run the heat seaming iron slowly over the hot melt adhesive, taking care to not burn yourself.
Press the carpet edges on one side of the seam down onto the hot melt adhesive, causing them to join and adhere. Work in small patches, smoothing the carpet down as you go. The overlap will smooth out with the seaming iron, leaving you with a straight edge.
Moving to the second edge of carpet, pull it taut before repeating the process of heating the hot melt adhesive and smoothing the edge down.
Leave to cool, and for best results, do not walk on the carpet for 24 hours while the adhesive sets.