How to write dialog in a journal?

The same way you would write it anywhere else.

Seconding Bufty.

I keep a daily journal and record conversations in two different ways. For the mundane ones, I summarize. For the interesting ones, I summarize the boring stuff and quote the interesting stuff verbatim along with narrative description.

I've also read quite a few histories which quote from old letters and journals and those will often also relate fragments of conversations verbatim.

I think readers' suspension of disbelief would carry if you chose to share a conversation in a journal as if it were a normal part of the story. If you want to go more authentic, however, it appears that people abbreviate conversations in journals more than authors tend to. They'll summarize parts but the key exchanges will be quoted.

All fiction is artifice. Putting verbatim dialog into a journal/diary/letter may seem more artificial than summarizing, but it's a long-established convention in fiction that readers generally accept without any problem.

And if you want to cover scenes via journal/diary/letter that are too important or interesting to just summarize, there's really no alternative.

Hmm, when I was an angsty teen and kept a diary/journal, I sometimes recreated the actual conversations I'd had with people--my parents (usually fights), or my boyfriend (sometimes fights, sometimes romantic). Other times I summarized. As others have said, it depended on how important I thought they were.

Which, when you think about it, is the criteria we use in novels for showing conversations via dialogue scenes versus summarizing the gist of a conversation.

I'd think how a person may present such in their journal would also be a function of the personality of the journal writer. An angsty teenager would keep a different kind of journal than an expedition leader or an earnest scientist who is recording his/her thoughts and experiences for posterity. But a big part of these differences would be in what kinds of interactions they considered important enough to record verbatim.

If I were in your place, I might get my hands on some actual journals from people who were in situations that are similar to the journal writer in your story. See how they handled these things. My guess is that there will be some variety, and there's a way to present it in a way that works for fiction without suspending disbelief.

I'd probably handle journal entries like I would handle one character telling a story to another character. And if there's dialogue it would be short (the best glorious parts).

Maybe this just Halloween proximity talking (or the fact that I just reviewed the movie Shadow of the Vampire on my blog), but I'd recommend reading Bram Stoker's Dracula if you want to see an example of how best to do this. The entire book is written in epistolary format, consisting of letters and mostly journal entries. There's a good amount of dialogue, so you'll have plenty to work with.

I write the same way in a journal that I write in fiction. Format, dialogue or narrative, is there for ease of communication, so I use it in a journal.

I do think it's good to realize there should be a difference between a journal and a diary.

I think the best way to approach something like that is to have a strong feel for your character's voice and how they would describe a conversation. I have a few characters who are very particular about accuracy, for example, and would probably attempt to recall conversations verbatim. I also have some characters who would be more than comfortable jotting down a quick summary of the conversation, and then expanding upon the "important" bit of what was said.

I think it really just depends on the character.

I would suggest searching around and looking for examples of how people have kept journals, and find out if anyone has a particular style that you think would be a good fit to try and emulate for your entries.

Lacking that, experiment with a few different formats to try and get something that feels write for how you need it to fit into the story.

There are novels and short stories out there written in journal format. Some are based on a character finding the journal, and then the story become what's in the journal.

Unlike a diary, a journal's real use is to tell a story.

You might want to try writing a few journal entries (pen and paper) of you own life over a few days and see what that feels like and what you would emphasize or glance over. Then write one or two for your character in their voice (again in pen and paper). Good luck with your story.