[yuriyuri]

The majority of words in kanji will be 1 or 2 kanji in length.

Also you can help split up words by recognising grammar in between the words.

For example:
自民党の長期安定政権

Can be broken down into:
自民 + 党 = Liberal Democratic Party
(I split up 自民 and 党 because 党 can be used as a suffix for a political party)
の - Particle
長期 - Long time period
安定 - Stability
政権 - Political power

This is how I split up words most of the time.

Also the more practise you get with reading the easier it will get over time.

The only things I have trouble reading are place names, like: 軽井沢 (Because I always think of completely the wrong readings and don't realise it's a name)
And of course sometimes I get confused with the names of people, but that's really just because I haven't read very many names.

Edit:
I suddenly just remembered that sometimes you might encounter four-character idiomatic compounds (四字熟語)
These ones aren't split up into 2's (As implied by the name)

A few examples are:
一石二鳥
十人十色
一生懸命
etc.

If you use a dictionary you will find the meaning very easily.
So sometimes it's worth trying to look up all four kanji as a whole "word" instead of breaking it into two.
Unless of course you somehow come across a stupidly rare one like I did one time (口誅筆伐)

But the large majority of the time you can break things down like my example at the top of this post.