Hello!
I'm a computer technician and I have done this many times. Usually the laptop does have a CD-ROM drive but it is rather useless since it cannot read mosts disks due to wear. The trick is to put the hard disk in another computer, format it as FAT (up to 2GB) or FAT32 (larger than 2GB), make it bootable and copy all the Windows 98 files in a folder. The best choice would be to connect the hard disk directly inside the host PC using an adaptor from 2.5" IDE to 3.5" IDE. The IDE cable plugs on the adaptor. Disconnect host hard drive to avoid mistakes and boot the computer with Windows 98 CD. Select to start computer with CD-ROM support instead of starting setup and use appropriate DOS commands (FDISK, FORMAT) to delete any existing partitions, make a single Primary partition occupying the whole drive and set it to active (bootable). You could use Powerquest Partition Magic or other such tool to make things easier. Also make it bootable with the SYS command that transfers the appropriate system files in the disk. In theory you could do the same by connecting the disk with a USB adaptor, but then the host PC must support booting from USB and then making the disk visible in DOS.
After you format the disk and make it bootable by transfering the system files, you can switch off the host PC, reconnect the host hard disk and make sure you boot into Windows from the host hard disk. The notebook hard disk will be E: or whatever is the next available drive letter. Just create a folder W98SETUP and copy all Windows 98 files in that folder. It is a good idea to include any drivers in a folder DRIVERS, so you won't have to download them within Windows 98 which is more tricky to do. Extract any archives to a subfolder, so you won't need WinZIP or WinRAR. If you want to use it, last version supported by Windows 98, I think, was 10. Make sure you include it in the disk as well.
Put the hard disk back to the laptop and switch it on. If everything is done properly, you should see the DOS prompt C:\
Use the following commands:
CD W98SETUP
SETUP /IS
Follow the onscreen instructions and input the CD key (serial) when prompted. Proceed Windows 98 installation as normal. As you may know Windows 98 search for Windows 98 CD-ROM every time it tries to install a new driver or enable a feature. No problem, any file you need is in W98SETUP, of course you avoid deleting this folder after completing setup, just in case, unless you have too little free space. Most USB Flash drives 2GB or lower have their own Windows 98 driver, so you can use them. There is also a generic USB driver that even works in Windows 95! I can send by e-mail if requested. USB CD-ROMs also have some driver to make it work in Windows 98, check manufacturer's site or try generic driver.
Non-latin warning: In Windows XP and newer, if you mess with international settings, you can simply correct them from Control Panel and reboot. THIS IS NOT TRUE IN WINDOWS 98! Make sure you install Windows 98 in CUSTOM mode and double-triple check any setting BEFORE proceeding, otherwise you may have to format the disk and start over! For Greek support for example, select code page Greek 737 (437) for full Greek compatibility. If you select Greek 737, it won't display all text properly and you will experience compatibility problems. The same might be true for other languages, so make extra sure you get it right before proceeding with setup.
Networking tip: Windows 98 weren't so advanced, so if you cannot connect to the internet with auto settings (DHCP) try manual settings. Especially internet connection sharing ("stealing" internet from another computer with a cross LAN cable) doesn't work in automatic settings, both computers must be set manually (the IP of one is set as gateway to the other and vice versa and DNS are set to those of ISP). And don't forget there is no Windows 98 Wi-Fi interface, for wireless networking you must use the WLAN utility! Other than that, I have successfully networked Windows 98 with XP, Vista and 7 and I could see their files. To enable sharing you must share at least a folder, and of course all computers must be set to the same workgroup (eg WORKGROUP or MSHOME). Only computers with at least a shared folder are visible when browsing the network. Computers that do not share a folder may see other's files (depending on other settings) but they are invinsible in the network. In Windows Vista and 7, disable sharing with password, since this is not supported in Windows 98. If a shared folder is inaccessible, go to Security settings, add user Everyone and check all boxes to give full access. Network printers must first installed locally in eg LPT1, since host cannot provide Windows 98 compatible drivers. After the drivers are installed, you can browse the network, install the printer and then delete the local instance.
Extending Windows 98 capabilities: Some guys created a custom Windows 98 kernel that adds Windows 2000 and Windows XP compatibility! OK you cannot have full compatibility as with the real Windows XP, but you can install and use several programs (eg new Mozilla Firefox browser) in Windows XP compatibility mode! As you may know Windows Internet Explorer 6 is outdated and most sites (using Flash) crash. It won't allow you upgrade to IE 7, let alone 8, even in Windows XP compatibility mode, so your best bet is to install Mozilla Firefox! Don't forget to disable hardware acceleration in Firefox, or it will be TOO slow and some graphics may not display properly. Also make sure you install latest Flash Player to see most sites. The extended kernel is here:
http://kernelex.sourceforge.net/
I hope that helped.