Read this article that goes way over my head but seems relatively well-written. The idea that interstellar travel could be achieved by folding space has long been predicted and researched. My favorite use of this technology was in the film version of "Lost in Space," where they were to travel between two "portals" instantaneously (obviously didn't work!). Side note...this movie contained a young version of the warm-to-the-touch actress Lacey Chabert. Click that link at your own discretion.
Anyway, the massively massively massive amount of energy required to fold space is currently contained in a relatively familiar object: a star. This is what Dyson was getting at when he suggested his Dyson Sphere, which was basically a giant solar panel around a star, capturing 100% of it's output. Currently, the Earth uses less than 1% of the Sun's total output...and of that, humans capture less than .01% with photovoltaics.
Now, obviously there is no point to travel to a faraway star system if that star is shrouded in solar panels and can't provide energy for the local planets, so the best use would be to find a habitable planet that orbits a binary star system and build a Dyson sphere around the non-essential, smaller star, then use that energy to power the massive portal that would fold the galaxy and connect it to a far away point. Do this, and you don't need to travel faster than light.
What the hell am I talking about? Imagine a big, square brick of sponge. This is "space". If you put your fingers on opposite points of the sponge and push them towards one another, you have effectively folded space. It takes energy from your arms to hold the sponge in that configuration. This is the energy that would be harnessed by the Dyson Sphere, and used to power the portal.
Or at least, that's how I'd do it.
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