I'm going to install Netbook remix on my 4GB flash drive. Will 4 GBs be enough? How much space will be left for data?
For a proper install 4Gb might be a little tight, though workable depending what programs you intend to install. When I install 9.10 on an old PC with an old ~4Gb spinning-disk based drive (to test the machine before giving it away) I think there was around 1Gb left. This included having some swap space, so if the target machine(s) has plenty of RAM you can save a little space by not using swap. Depending on what you plan to do, this might be more than enough space for you.
Making a USB install of the live CD with persistent storage may be a better option if more space is needed - this way most of the core installation goes in the compressed (squashfs) file with changes and new data going into the copy-on-write file used for the persistent storage. This means you will make much better use of your limited space if the bulk of what you want is in the standard install set found on the live CD. You might even fine some things run faster this way if your USB drive reads slowly, as the compression will reduce the amount needing to be read from the drive in some circumstances. You can make such a USB boot drive directly from the live-CD on any machine, following one of the many online tutorials like this one. I have a UNR install on a 2Gb stick this way - it is my emergency backup system for in case my netbook's main drive (or the filesystems on it) develops a fault.
Another option may be to use lubuntu instead of Ubuntu Desktop or UNR, this creates a more minimal system using less disk space and using less RAM and CPU resource by default but you can still install all the full-fat apps like OpenOffice if you need them - even after adding a few of these the space used may be noticeably smaller than a default UNR install.
Of course your flash drive can be easily reformatted so you could just try a few of the above options in turn to see which fits your needs best and all you lose is the time take to install and try each (this might not be wasted time either, as it could be useful learning or confidence-boosting experience!). If you are worried about your flash drive slowing down (as SSDs do over time due to block fragmentation caused by wear-levelling algorithms not being filesystem aware) due to the excess writes from trying a few complete installs on it, you could always install a free virtualisation solution like VirtualBox, create a couple of VMs with 4Gb disks using that, and try all the above to compare results before committing a solution to your flash drive. You'll probably find this quicker too, even factoring in time to learn the basics if VirtualBox,as installing to a VM running on a standard desktop/laptop drive will be a lot quicker than installing to a slower flash base USB stick.
I was curious and ran a quick test "live CD" install of 10.04 on a spare 2Gb USB stick. This boots much slower than 9.10 does in similar circumstances (same size and speed of stick, running on the same netbook). Using as much space as possible for the persistence file gave "1.2G total, 71M used, 1.1G free (7%)" on the resulting root filesystem once booted. Running
So a 2GB stick probably isn't viable used this way long term, but I expect a 4Gb one would be (depending on expected use pattern, of course). Don't use all the free space for the persistence file, leave at least a few Mb in case you want to try update the kernel later. A proper install will take more room initially, going by Shiki's estimate of "up to 2.5Gb", but probably not much more in the long run (actually, possibly less in the long run especially if you remove default packages that you don't need) and it may boot faster.
Ubuntu takes up about ~2.1gb at default (max 2.5gb). If you install some stuff... well.. calculate. You will have some space but not much. Try Crunchbang/Absolute/Lubuntu linux or something lightweight. (Or just get a bigger drive, they almost throw it at you for free.)