In rhymes, is only the sound of syllables concerned (see: Rhyming in modern Mandarin), or also the tone is somehow involved?
Traditional Chinese poems involve some complicated concepts, which can be written for a big book. In general, both sound of syllables and tones concern.
But it could be very different from modern Mandarin, depending on the characters. In addition, both sound and tones could be different.
Now here's the short (but far away from complete) story:
- Traditional poems have to be written with severe discipline, most characters should follow one certain tone family according to the poem format. Only some of them are free.
- There are two general tone family: 平 and 仄 ze4。(level tone and oblique tone)
- Most first tone and second tone Mandarin characters are of level tone family. While most of the other two are of oblique tone family.
- But there are too many exceptions... due to long history of Chinese, the tone continue changing over time. Only refer to professional tools or books can we tell if one character is an exception. (btw, actually there are five tones used in traditional poems, but you don't need to know another long story.)
- Finally we can talk about sounds or syllable rhymes. There are dozens of sound families/groups, and each character belongs to one family. Generally you can use characters to rhyme from only one family in one poem. (But in @Ringil's answer there is an acceptable exception.)
- Usually characters from one family share the same vowel/final（韵母）.
- Be careful about syllable rhymes. The count of these families is much more than Mandarin finals. So even if two character have the same final in Mandarin, it could belong to different sound families.
- And again, some character's final have changed over time...
- Even in Chinese history, poems from diffenrent dynasty have some little differences in rhymes...
But don't panic! None of the above is neccesary to enjoy poems, though knowing more about sounds and tones could help.
At last, If you can read Mandarin, I strongly recommend Professor 王力's master piece: 《诗词格律》(Poem Discipline). It is not a big book, but the very essential part of traditional poems.
Only the sound matters. For example, the famous Tang dynasty poem 《清明》by 杜牧:
The second and fourth lines rhyme but have different tone (2 vs 1)