Phonemes don't just randomly combine to make a language. They have to be arranged according to certain rules. For example, if you take the phonemes out of "complexity" and rearrange these randomly, you don't get an English word:
/k@mplEksIti/ <complexity> /ksIlmp@kitE/ (approximately pronounced "kuh-silm-puck-eat-eh")
So what is phonotactics? Basically, it tells you what sounds can go where, and what sounds can't. In English, for example, a word can begin with spl- (split, splash), and spr- (spray, spread), but not slr- or srl-, or slp- or srp-. That's just how it works in English. On the other hand, words in Russian can begin with vstr- and dn-, which you wouldn't be seeing any time soon in English. Words in Japanese, on the other hand, can't begin with spr- or spl- or even sp-; it has to begin with a single consonant, or none at all. (When Japanese people pronounce "splash", they tend to say "suh-puh-la-shuh" /s@p@l&S@/ — For comparison, try pronouncing the Ukrainian city of "Dnipropetrovs'k".)
Syllable Structure Edit
So how would you make these constraints up for your conlang? Well, the earlier section on syllables can help. Start by dividing your conlang's phonemes into different categories and then defining which categories can combine with others in what ways inside a syllable.
For instance, Toki Pona defines its allowed syllables as V or CV(n), where C is any consonant and V is any vowel; "n" represents itself /n/; and the parentheses mean "optional". So syllables like /sen/ and /jo/ are allowed in Toki Pona, but /stan/ and /pit/ are not. Konya allows C(S)V(N), where S is a semivowel (/j/ or /w/) and N is a nasal (/m/ or /n/). Vorlin allowed syllables of the form C1VC2, where C1 is any consonant in Vorlin except /N/ and C2 is any consonant in Vorlin except /h/.
English itself does not have simple phonotactics. It allows (C)(C)(C)V(C)(C)(C)(C)(C). "Strengths" for example is one of the longest allowed syllables even though it doesn't fully use up the allowed coda. But there are still constraints on what consonant clusters are allowed in the onset and coda.
How would you create your own syllable structure? By selecting what sounds can occur in the onset, nucleus, and coda of a syllable (remember back to the section on syllables). You will notice that all the examples above have V (any vowel) as their nucleus and that it's never in brackets (and thus not optional).
Viable consonant clusters Edit
Another way to specify phonotactics is to make a list of all consonant clusters that are allowed and then, by implication, you should know which consonant clusters can't appear in your language. For example, in the conlang Quenya, the consonant clusters /mb/, /nt/, and /lm/ are allowed, but the consonant clusters /pn/, /rl/, and /ln/ aren't.
Of course, these two ways to describe phonotactics are not mutually exclusive; one can perfectly state that, given the restrictions of syllabical structure, there are certain clusters that don't happen and others that do.
http://clas.mq.edu.au/speech/phonetics/phonology/syllable/syll_phonotactic.html A nice text about phonotactics. Could be used to improve this page.