Any slide rule intended for use in normal science/engineering calculations will have various scales on it, but the underlying principle is that all are logarithmic. The rule makes use of the fact that Log (a x b) = Log (a) + Log (b).
Anyhow, to get to the matter in question, you'll need to make use of the C and D scales. C will be on the bottom of the sliding portion and the D scale will be directly below it on the body of the rule. If you want to be able to measure dimensions off, say, your 7mm scale drawing and use them to construct a 10mm scale model, then start by positioning the hairline on the sliding cursor (The transparent thingee that slides up and down the rule) directly over 7 on the D scale. Now move the slide so that 10 on the C scale (located at the RH end of the slide) is directly under the hair line as well. Now you can make a measurement on your drawing with a standard metric ruler, or pair of digital calipers or whatever. Let's say you measure a feature on the drawing is 23.8mm long. Move the cursor so that the hairline is directly over 238 on the D scale. The hairline will also be directly over the 'equivalent' measurement on the C scale. I make it 340, so a bit of common sense tells you that the answer is 34.0mm. As an earlier poster has pointed out, a slide rule has no decimal point, so you need to estimate the 'order of magnitude' of the answer. i.e. where to put the decimal point. If you slide the cursor to the left hand end of the D scale you will see that 1000 on the D scale corresponds to about 1428, or a smidgen under 143, which corresponds to 1.43286, which is 10/7. Effectively you're using the slide rule to multiply any measurement on your 7mm scale drawing by 10/7. The annoying part comes when you have to deal with a measurement which falls between about 78 and 90, or 7.8 and 9.0, or..... These measurements fall on the D scale where there is no part of the C scale directly above it. If you have a slide rule like mine you can see that the C and D scales both have little extensions to 9 on the left and 112 on the right, but for those rogue numbers in between there's nothing for it but to align the cursor over 7 on the D scale and shove the slide to the right, so that the 1 on the LH end of the slide is aligned over the 7. Now you can read that e.g. a measurement of 84mm on your drawing corresponds to 120mm on your larger scale model.
One way to avoid the necessity to shuffle the slide is to make use of the A and B scales. These scales are the same as C and D, but half size, so each scale runs from 1 to 100, instead of just 1 to 10. The up side is that you can avoid needing to shuffle the slide, the bad news is that resolution is now only half as good.
Many years ago I used to use my slide rule to convert measurements taken from a 1:48 scale drawing for use on a HO scale model. It was just a matter of aligning 871 with 48. It really doesn't matter which number goes on which scale, so long as you're consistent. The only complication is that if, in this case, 48 on the D scale is aligned with 871 on the C scale, then measurements taken off the drawing are entered on the C scale using the cursor and the equivalent measurement for the HO scale model are read off the D scale. If you think about it, you'll see why this is so.
As you can probably grasp from the foregoing, it's simple enough, but still a bit of faffing about, which is why I tend to use an electronic calculator these days. For a case like yours, I'd just calculate the value of 10/7 and store it in the calculator memory. Enter your measurement, then press X M and the measurement for your larger model flashes onto the screen.
Happy calculating.....