Hello. I am making a web server and would like to use Slackware as the OS. The last linux OS I installed was Fedora, so it automatically took care of the partitioning.

I have a good idea of how to partition using fdisk from Googling, but I couldn't find any recommended sizes for partitions. I realize that this varies based on numerous factors, but I would like some numbers, at least as a ballpark estimate (something I can go by).

I am creating the following partitions:

/boot
/tmp
/
/var
/usr
/home
swap

The hard drive capacity is 3.2 GB and I am making the swap partition 48 MB because I only have 24 MB RAM (It's an old computer). Thanks in advance.

you do not need to make all those partitions. You can make a /boot if you are planning to dual boot with another distro (which by your hard drive space, you are likely not). You can make a /home so that data and preferences persist, but sometimes it is cleaner to save what you need and restore them with your head. Swap looks good.

My rule of thumb is that if you do not know what size to make the seperate partitions you should not make them.
About the only time I create extra partitions is on a server.
I find and read some articles that discuss this, check sizes of those filesystems on current running systems, consider what the difference might be with server usage, and guess.

Hy i had a slackware webserver with ssh and some user. I also had a wide range of partitions. I just post them so you have some figures. Nearly all of slackware 9.1 packages had been installed beside any Desktop system

1.7G for / with 4% used
83Mb for /boot with 5% used
894Mb for /home with 1% used
447Mb for /tmp with 1% used
1G for /usr with 44% used
350Mb for /var with 22% used

Like you see root was far to high, but if you need a Desktop it might be reasonable. Home was only filled with my own two users, so way oversized. Should bee enough for 10to 100 users. tmp: who knows what you are to install. usr is the only real used spaced. var depends on your logging avtivity. I just would give it 1G so you can store a lot and for long time.

Hope it helps somehow.

edit: Did not see that you only had 3G space. But i think you can ajust the numbers to your space....

I would make 3 partitions:
48 MB swap (you figured that out well).
1.5GB / the system (maybe 3 GB, maybe 1 GB, it is a matter of taste).
the rest /home.
If you are going to install a new distro or a fresh install for an update, only / will be newly formatted & installed.

A trick I use:
Not only /home I want to preserve, but /etc and /usr/local too.
the trick is: make dirs /home/etc and /home/usr/local
Copy the stuff of /etc to /home/etc
#cp -a /etc /home/etc
# rm -rf /etc
# ln -s /home/etc /etc
Same trick for /usr/local

Only one extra partition with 'stuff to save'.
Works fine for me on an old computer.
The advantage is: One partition with all stuff to preserve, not the overhead of more extra partitions.
Hope this helps.