First off if you are using layers in photoshop (PS) you are going to have to either merge the visible layers or flatten image. Just make sure that you save this merged file under a different name (like: fileMerged.psd). And some good advice is to save often, each major change should be saved with a different file name (like: file1.psd, file2.psd, ect.) in case you need to make any changes. You can always delete earlier file names if you've reached a stable design to save disk space.
Once the file is merged/flattened save it as JPG or as suggested use the 'save for web' export feature. I normally don't use the splice tool myself, I find I have greater freedom if I just use the marque tool. Again save each individual cut image in an 'images' folder in which ever file format you choose. JPG has been suggested, but their are others such as GIF and PNG. Look at Adobe's help or what the files look like when saved with different extensions to decide which one you want. Generally images that are transparent or have few colors and text are saved as GIF. JPG doesn't compress text very well, but works better than GIF when there are many colors, such as gradients for example.
That's it, the web development team should be able to do the rest. But, I would advise working closely with them to ensure that the graphics you design will be easy to implement. Design your graphics around what they need or suggest, it'll make the project smoother in the long run.
Ideally, I wouldn't use FrontPage or anyother WYSIWYG editor, but that'll be an experience that your team will have to learn from .