First, a disclaimer: this is a question many are asking, despite the timing of it feeling off. Carrie Fisher has passed and the impact of that death on people, on lives, is by far the most important thing that needs to be observed. May she rest in peace.
Next, what does her passing mean to the Star Wars franchise?
Eventually, the question will have to be answered; as a lynchpin of the saga, her being gone will have an impact cinematically; with General Leia being an important part in Star Wars: The Force Awakens, and likely an even more important one in Star Wars: Episode VIII, it's a valid question.
Episode VIII wrapped filming several months ago, and this most likely won't impact that film at all, or at least minimally. We don't know what the plot of that film is, but know that Leia, Fisher's character, has to play a fairly major role in it; her husband was killed by her son in The Force Awakens, and she's going to have something to say and do about that.
The film is still in editing and post-production, so if there's a way to properly, with respect and care, remove Leia from the board without drastically changing the story, it will likely be done.
Rather than simply killing the character on-screen because the actress died off-screen, Lucasfilm, and writer/director Rian Johnson, will probably try to work out a way to make Leia's journey come to a satifying conclusion.
Of course, if the character was already meant to pass in the movie, that brings them to another complicated question and course of action; it will be just under a year since Fisher's passing when the movie comes out, and that would be a very difficult image to see on screen for all involved; actors, fans, creatives, family - it's hard to think that would ever be a scene possible to stomach. Conversely, having the character Leia die off-screen could feel like a disservice to the character; it's a lose-lose situation.
As for the future films, like Episode IX, a bit of creative writing from Johnson (who is helping on that story), that movie's director Colin Trevorrow, and the rest of the Lucasfilm team is most likely. The use of CGI to recreate actors in Rogue One was certainly precedent, but that was done years after Peter Cushing's death, and with his estate directly involved. Don't expect the same to be done in the case of Leia; some unused footage from Episode VIII for a proper goodbye is the closest to that we're likely to see. Likewise, don't expect the character to, in any way, be recast. While that was the smart and only course of action for a film franchise like Harry Potter and the character Dumbledore (due to the stories having been written in the books), Leia is Carrie and Carrie is Leia - she has forty years of playing the character.
The only other possibility is that there's unused footage of Leia shot for Episode VIII that could be somehow repurposed for Episode IX (again, assuming the character was meant to go into that episode and story) to help give Leia a fitting conclusion to her own journey. Without knowing the plot of VIII that's impossible to really figure out, though.
Ultimately, Lucasfilm is in fairly uncharted territory here, and it's going to be a very difficult year; while trying to get excited about Star Wars: Episode VIII at events like Star Wars Celebration Orlando in April, there will be a massive hole in the Star Wars family. Rian Johnson, Kathleen Kennedy, and the Lucasfilm team have a nearly impossible task ahead of them. Carrie Fisher is irreplacable, infinitely moreso than the also irreplacable Leia Organa.