Reciting Asmaul Husna (the 99 Names of Allah) involves calling upon Allah by His beautiful attributes. You can recite them sequentially as a daily Dhikr, or incorporate specific names into personal supplications (Dua) that align with your needs.
The advice below is extracted from Dua's for the contentment of the Heart
When wishing to recite ALL the Beautiful Names of Allah, begin by saying:
هُوَ اللهُ الَّذِیْ لَا اِلٰهَ اِلَّا هُوَ الرَّحْمٰنُ الرَّحِیْمُ
He is Allah, other than whom there is no deity, the Most Gracious, the Most Merciful
Then, continue reciting the names until the end. But the last letter of each word should be recited with the vowel Dhamma (Pesh) and joined to the next word. But when pausing to take breath the last letter should be recited with Saakin (jazam) and the following word should be started with.
When adopting a particular Name as wazeefah (which one intends to recite daily) add يَا before the Name and eliminate the ال. For example, اَلرَّحْمٰنُ will be said as يَا رَحْمٰنُ and NOT يَا اَلرَّحْمٰنُ.
A learned Aalim should be consulted when one experiences any difficulty.