As already said, in order to push out the exposure time, you need to make what the camera is seeing darker. Which is done by neutral density filters.
These basically come in 2 forms. Circular, which screw onto the end of the lens itself and match the round end of the lens. Or square. You attach a filter holder onto the end of the lens and then slide square filters into the filter holder. There are adapters which join the holder to the correct diameter of lens. That way you can have more than one filter attached the end of the lens.
I would recommend going down the route of the square + holder , because by just changing the adapter on the end to fit whatever lens you are using, you can use all of your filters across all of your lenses.
There are 2 main sizes of square filters ... I'd recommend you go for the larger one at 83mm ... that way you can attach the filter onto wider and physically larger lenses.
As a basic place to start and get them, 7dayshop.co.uk do a good selection of holders and filters in the standard sizes. Its not pro-range stuff, but its good enough to learn with and if you really want to go further, then you can buy the expensive stuff later.
Some other things to consider:
A neutral density filter will darken the whole picture. In the type of shot you posted, its quite often the case that the sky is bright and the foreground much darker. A graduated ND filter can be used to darken just one half of the picture ( such as the sky ) to prevent over-exposure of the sky and allow the darker foreground to remain visible. Using a square filter also means that you can slide the filter up and down in the holder to adjust the fade point to match the scene as required.
Another filter worth considering would be a circular polariser. They can add a lot of the type of photograph you've posted too. ( plus they are quite dark filters and act as an neutral density filter at the same time. ) I'll let you read up about polarising filters in your own time.