A contradiction between timeframes is not a markup error but its normal condition. The daily chart can be in an upward structure while the hourly is in a downward one, and both statements are true.
The reason is the same as for degrees within one chart: a pullback on the higher timeframe fits entirely inside the lower one and looks there like a full move with breaks of its own.
The reading order
The conventional one is top down, and for good reason.
The higher timeframe sets the frame: where the current move sits and what would have to happen for it to change. The lower one shows what is going on inside that frame right now.
Reading the other way round is harder: from the lower timeframe you cannot see whether the current move is a trend of its own or a pullback inside a larger one.
How many timeframes to use
Two or three is enough, and they are better noticeably apart in scale. Adjacent ones — hourly and four-hour, say — show almost the same thing, and the third picture adds nothing but confidence.
A typical pairing: one for direction, one for detail. More than three usually means one of them will confirm whatever you already think.
Where most mistakes come from
A break with no timeframe named. "Structure is broken" is an unfinished sentence. On the lower timeframe it breaks constantly; on the higher one, rarely.
Carrying a level between timeframes unchanged. A level that matters on the daily chart will be pierced and recovered dozens of times on a five-minute one: what is a single event above is a series below.
Hunting for confirmation. Go low enough and confirmation exists for any idea — there are many lower timeframes, and on some of them structure will point the way you want.
What multi-timeframe analysis does not give you
Two timeframes agreeing does not make a conclusion truer. They are not independent: the lower one is the same series cut more finely. Matching directions mean only that the current stretch is moving the same way as the one containing it — and say nothing about whether that continues.