OSDev.org

Hey guys! What would be good documentation for operating system development with FASM? I can't really find anything on the internet. Please help.

It's the same concepts as using GCC or NASM; the difference is just that the code is written in a different language (and therefore is tightly bound to one CPU family architecture, x86/x86_64 in your case.) FASM uses Intel syntax (like NASM) and not AT&T. If you want to learn the various feature of the assembler itself, consider reading the documentation.
EDIT: IMHO, FASM is an excellent assembler for doing OSDev entirely in assembly language, because it's easily portable to other systems. My OS is written entirely in FASM-style assembly.

Is the documentation really good for learning about the FASM syntax? Can you use all the instructions? By the way, how would I print a string in 32 bit? The tutorial on the Wiki has lea instruction and it doesn't work.

You can use all instructions supported on the CPU you're using. You may need to detect specific instruction sets using CPUID; for example, SSE, AVX, VT-x and other things are not present on all CPUs and you need to detect their existance.

Copying and pasting is a very bad practice, even for a beginner. It doesn't get you anywhere useful.
Instead, read on the theory of printing to the screen. The theory is that the screen (in standard VGA text mode 0x03) has 80 columns and 25 rows and the video RAM starts at 0xB8000. Each video RAM "entry" is a 16-bit word, the low byte is the character to display and the high byte is the attribute. The low 4 bits of the attribute is the foreground color. The high 4 bits of the attribute is the background color (or bit 7 may be the blink bit, it depends on how you configure the VGA controller, but this is off-topic.)
Knowing that the screen resolution is 80x25, you should be able to calculate the address of a specific character on your own, knowing that each character takes up two bytes of video memory (i.e. at 0xB8000 is the character and attribute at position 0, 0, at 0xB8002 is the character and attribute at position 0, 1, etc...)

I don't think you did your homework/research. The documentation is reasonably good. There's also a forum, where you can ask questions and get good answers. There's even a section specifically dedicated to OS Construction.

If it helps at all, FASM syntax is very similar to that of NASM and YASM. I actually support all three assemblers for compiling the assembly code generated by my Smaller C compiler. I only need to do the following when translating from NASM syntax to FASM syntax (the translation is done by a separate tool (n2f), the compiler emits asm code in NASM syntax):

• combine fragments of the same section under the same section header (FASM puts fragments into separate sections, so without combining you end up with multiple .text (or .data or .bss or .rodata) sections in the ELF file, which isn't something Smaller C expects; NASM combines section fragments for us)
• 'section .text' -> 'section ".text" executable'
• 'section .rodata' -> 'section ".rodata"'
• 'section .data' -> 'section ".data" writable'
• 'section .bss' -> 'section ".bss" writable'
• 'section something_else' -> 'section "something_else"'
• 'bits 32/16' -> 'use32/use16'
• 'alignb number' -> 'align number'
• 'global symbol' -> 'public symbol'
• 'resb/resw/resd number' -> 'rb/rw/rd number'
• 'extern symbol' -> 'extrn symbol'