The name Virginia Woolf likely conjures the image of an important cultural figure, a significant writer, but one with an intimidating reputation. As such, readers may either stay away from her work or approach cautiously, expecting something wilfully obscure and deliberately difficult.
The truth is that, yes, Woolf's writing can be a challenge and the reason for that is mostly because it's so unique. We're used to plot- or character-driven novels, where things happen in some semblance of order, where there's narrative resolution, and often where you can dip in and out with ease. The stream-of-consciousness style that Woolf employs in "Mrs. Dalloway" (1925) shirks conventions and as a result it can be a disorientating read.
But that doesn't mean it can't be enjoyable. The thing to remember with "Mrs. Dalloway" is that it is not a plot-driven novel. As other reviewers have accurately stated, this is not a page-turner, not something to marvel at all the ingenious plot twists and turns. So why read it? The main thing I took away from "Mrs. Dalloway" was how much about the interior it is, and consequently how personal and intimate it feels. It's not "Mrs. Dalloway went up the stairs and sat down." It's all about inner thoughts, inner feelings, and as such this stream-of-consciousness style works wonders. We don't think in ordered sentences most of the time; our thoughts flit from one thing to another and we set off trains of thought and memory and memory association. The same is true of the writing in "Mrs. Dalloway"; there will sometimes be unexpected interjections and abrupt changes of thought process, which mimics our real human thought process.
Of course, action does take place - there are walks in the park, collecting flowers, sewing - but it's all filtered through the interior. It can be confusing to determine who is "speaking," as Woolf jumps between characters and they rarely have clearly-defined voices of their own, but that way it does feel more natural somehow. One moment we could be "in" Mrs. Dalloway, then she thinks of Peter Walsh, and suddenly we're "in" Peter Walsh, so to speak. It's a unique approach; much has been made of the revolutionary style. Whether it's relevant as 'revolutionary' today is immaterial - it simply works, regardless of whether Woolf originated it or not, and regardless of when it was written.
The other main element to note is Woolf's writing style itself. Her use of language is rich and beautiful, and she articulates feelings in a vivid, imaginative way that the reader can fully comprehend and relate to but still marvel at the imagery she is using. There will be occasional metaphors or sentences that stop you in your tracks for a while because they're so well-drawn and creative, yet entirely in keeping with the mood and feel of the novel. (It also must be said that Woolf does have a sense of humour, and some of her observations and interjections here are softly funny and sometimes wonderfully absurd.)
It's a book really to lose yourself in. By that, I mean: don't come into it with expectations, and certainly don't come into it looking forward to something exciting and plot-based. The power is in the writing style, the intimacy, and the accurate portrayal and evocation of human thought process. One can read into the symbolism and exploration of WWI, mental illness, sexuality, and human disappointment, and they're intrinsic, but even if you don't consider the symbolism or the cultural context it's still a novel that weaves a spell, slowly but powerfully.
Sometimes, it's a taste thing: some people will 'get' the book and enjoy it, and some won't, and one person is no better for 'getting' it and vice versa. But what I would say is that if you just allow yourself to get into the novel, and allow the novel room to breathe, and don't compare it to other, more conventional texts, it might just surprise you. I was surprised sometimes how much I was enjoying it. Woolf certainly requires more concentration and effort on the part of the reader than some other authors, but the ultimate rewards can be very satisfying.