There are many ways to accomplish this in TMS WEB Core. Using tables for layout isn't really a thing anymore, thankfully. How you set about this will depend largely on how Delphi-like you want it to be.
One approach is to just use TWebPanels as you would in a Delphi app. Set the alignment of one to the top, one to the bottom, and one to Client and you'll get some variation of what you're after.
Another approach is to use TWebHTMLDiv components, though you can use TWebPanels as well. Here we're doing a similar kind of alignment but using CSS properties instead of Delphi alignment. Add three to the page. Set the ChildOrder to 1, 2, and 3 for the top, middle, and bottom. Set the ElementPosition for all three to Relative. Set the HeightStyle for the top and bottom components to Fixed with some value, like 75 or something. Set the middle component HeightStyle to Auto. It will then stretch to fit its contents vertically. Set the WidthStyle for all three to Percent, and set the WidthPercent to 100.
Another approach is to use CSS Flex. This is easiest if you use Bootstrap in your project. Adding the same three elements again (TWebHTMLDiv or TWebPanel), set the ElementPosition to Ignore. In ElementClassName for each, add order-1, order-2, or order-3 to set the order. Set the WidthStyle as before to Percent, and WidthPercent to 100%. The HeightStyle can be set the same as well, using Absolute with a fixed value. For the Form's Element ClassName property, add d-flex w-100 flex-column to get it to put the elements in order and stack them vertically.
There are about a thousand other things that can be done, but this gets you a header, footer, and middle section. How the middle section changes with excess or insufficient page height, and its own content, is where these start to diverge. You can also use CSS rules to apply a minimum height to the middle section so it doesn't shrink too much, or any number of other rules to get the contents of each to stretch or center themselves.
And we've not even gotten to scrollbars yet. Lots of options there depending on whether you want the footer at the bottom to be fixed at the bottom with the middle content scrollable, or if you'd rather avoid scrollbars and have to scroll to the bottom to see the footer. Likewise for content that is too wide for any of the sections - do you want the content to shrink down, wrap, disappear, etc. etc.
Nothing but options here.