Yes, you can compile it in a console terminal.
Open a Konsole terminal, cd to the directory you untarred you kernel source and configure it with "make xconfig". After this, I suggest you edit the Makefile to put an extra version. Then, start the compilation:
If all goes well, the compilation is not interrupted with "error" message, you have to put the things in place:
cp -a arch/<architecture>/boot/bzImage /boot/vmlinuz-X.XX.XX-yyyy
cp -a System.map /boot/System.map-X.XX.XX-yyyy
where <architecture> is your platform. For our ubiquitous PCs, it is "i386"., X.XX.XX is the kernel version you are compiling, for example, 2.4.26 and -yyyy is you extra version.
I suggest you to never compile a new kernel with the same version you are using. If you run into problems you can go into an unbootable system. To differ your compilation you have to edit the master Makefile, changing the contents of the "EXTRAVERSION" variable. Don't forget to put the "-" (hifen) to separate the version from extra version. If you enter "mycomp" you will have a kernel "2.4.26mycomp". If you use "-mycomp", you will have "2.4.26-mycomp".
After this you have to edit your boot loader configuration. Here, you need to know if your distribution uses grub or lilo. If you use lilo, you need to edit /etc/lilo.conf to include an alternate kernel. After edit it, you have to run "lilo" to reinstall it. If you use grub. you need to edit "/boot/grub/grub.conf" or "/boot/grub/menu.lst". Basically, in both cases, all you have to do is to duplicate the specification for the system which is booting and change the kernel name to the kernel you copied "/boot/vmlinuz-X.XX.XX-yyyy".
After all this done, reboot your system and choose your kernel at the boot prompt. If it doesn't boot, choose the other kernel and go to the top of this post.