I suspect you want to adjust the leading. By default ID uses automatic leading (which is shown surrounded by parentheses) and that in turn is set at 120% of the font size by default. In InDesign leading is a character level attribute (though you can set a preference to apply it to entire paragraphs), and you'll find the field in either the Character Panel or the Control Panel when working in text mode (set the Control Panel to Character mode by Clicking the A in the upper left corner). The leading field is identified by an icon that looks like two A's stacked on each other. You can enter any value you like in that field between 0 and 5000 points, or use another unit by specifying the unit when you enter the value. You cannot have negative leading (nor do I recall Quark having that ability). You'll also find a set of nedge buttons on the left of the filed that will increase or decrease the leading amount in 1 pt increments, and you can look up the keyboard shortcuts for adjusting leading in the Help files -- KB Shorcuts is the second to last topic inthe contents list, I believe.
Although leading is a character level attribute and you can have different leading amounts applied to characters in a single line of type, ID will always apply the largest leading amount in the line to the entire line.
Actually, I'm still not quite there.
What's the proper way of adding a bit of space between the first line of text and a text box (that I have put a frame on)?
Changing the leading in that particular line has no effect, so at the moment I'm putting in little empty lines of 1p height, which is not the best way of doing it, of course...
I think leading is a paragraph level attribute in Quark... Select the whole line if you want to change the leading for the line (though I don't really recommend this as future edits can have odd effects if the text reflows and you have different leading values in the same line -- much better to define the leading as part of the paragraph style and redefine the style, or if you need it for a particular line define it as a character style and apply it as a nested line style, a concept I think is lacking in Quark).
To change the first baseline offset, select the frame and open the text frame options. You can either add some inset to the frame, or switch to the first baseline tab and experiment with the various options.
I'm guessing you forgot to include the (final or only) paragraph return when making the leading smaller ...
ID will apply the same leading to an entire paragraph if selected in the preferences, or otherwise the same leading per entire line -- including the final paragraph return. If there are 'mixed' leading values, ID will use the largest.
Good typesetting does not use "empty lines" and you should not have empty paragraphs for spacing. To put space between paragraphs, use "Space Before" or "Space After" which is ignored at the top of a column, preventing unwanted blank lines at the top of a column or page.
The default "first baseline" setting in a frame in ID is Ascender which puts the text at the correct position so that the ascenders for the font will fall at the top of the frame. I believe this is analagous to the default in Quark. This position is generally higher than you would get if you choose "Leading" (an option not available as of Quark 6 when I stopped spending money on upgrades), and if you were to choose leading, the first baseline would rise or fall if you adjust the leading value for the line, whcih sounds like what you have in mind, but I really don't know what you are doing. I don't recall any way to adjust the position in Quark without either adjusting the top inset (as you can also do in ID) or using an empty paragraph and adjusting the font size, which is just bad, and used to drive me crazy on my first job when I worked on files created by other designers. As far as I can tell, at least as of Q6, the behavior of the first baseline postion in the two programs is nearly identical.
Many users who are switching from Quark to ID find they have difficulty at first because they continue to think in terms of the ways they used to work. Once you lose your Quark minidset you will find things much easier. The two programs operate quite differently in many respects, and I think if you took a survey here of people who use both they'd tell you that ID is more efficient and productive.
If you post a screen shot of where you want to adjust the space maybe I will understand better what you are trying to do and can give you some better advice. You can use the camera icon onthe web page to embed the screen capture in your post: