There are times where there's no one that's able to lead it, and it would be nice to be able to do so myself, but I'm not fluent in Hebrew but can read it slowly. What's the best way to practice for someone at my level?
Edit: a typical idea would probably be to practice over and over again. Not so much pronunciation but rather being able to read more quickly.
I had the same question years ago. I have used http://virtualcantor.com/
I liked the versatility of the site. But also its clarify for newcomers. I did not know the structure of the tefilla and therefore the way portions were broken up in a list of clearly named sound files really helped.
I even found it to be useful in teaching me the amidah for davening at home. I used to need ages to finish davening and I did not become faster by reading everyday. I dreaded the longer parts. Through the website i learned the melodies for the repetition and this gave me a melodic rhythm to help me understand the text. These were steps that helped me reach the level necessary to start as a shaliach tzibbur, but also to understand what skills in hebrew reading i lacked and how to overcome it step by step
The melodies are also a nice combination of melodic yet not too 'professional' for someone who has not been trained to sing. I just started with learning to read by practicing the parts that were sung. Now i can read and understand tefillah and use the melodies that are more traditional in my shul, but for me: it all started with virtual cantor.
In addition, my learning speed and quality have been greatly improved by studying small parts at a time not so much for singing, but so as to study the translation in my siddur. The siddur vocabulary is relatively limited so in the beginning many words were new, but after a short while it becomes easier to learn new parts, because you recognise words. This understanding is the "trick" of improving quickly. It also makes you more versatile: you can read 'surprise' sections easier, such as ad hoc added psalms for unforseen reasons, etc. Not only because you can read words. But understanding makes sure that you can improvise a melody that supports the meaning and syntax of what is written. The websites out there can be a useful crutch, but relying on them is a short road that is long. Complementing practice with understanding is the longer road that is short.
A final note: it is important to understand the basic halachot of the mincha service and tefilla in general. Knowing when to skip or add sections, why and when to kaddish is said and which type, etc. are all things that attribute to fast learning and practice. In the beginning it can be sufficient to have functional knowledge of the texts and melodies said by the chazan, but make sure to incorporate all three elements: singing, textual understanding, and halacha into your learning routine.
edit: given all the different styles and nusach out there, there are more (sometimes similar) weekday-nusach resources, such as wonderfully aggregated by offtonic.com
Ok, I will give some personal tips. Obviously there is no "source" for this. But I do often lead services myself (including this morning) and I am no "expert" really.
This is based around the repetition of the Amidah. The rest of what is said is just a few lines (and of Ashrei, end of Tachanun and end of Aleinu) and a couple of recitations of Kaddish.
Firstly, don't try to go faster than you can. Typically it takes me about 5 minutes to repeat a weekday Shacharit. Mincha is slightly shorter because you don't recite the Birkat Kohanim (and in my nusach, we also say the shorter Shalom Rav at Mincha). If it takes you 6 or 7 minutes that's probably not going to hold everyone up so much. If it takes you 10 minutes then that is indeed very slow.
The only section (assuming nusach ashkenaz) you don't normally recite is the bit after kedusha "l'dor vador nagid godlecha" so practise that part...
Stop and breathe: At the end of each b'racha, the congregation recites Amen and that is a chance for you to take a deep breath in preparing for the next B'racha. Some b'rachas are longer than others so you'll need other stops to breathe too.
Recite all of Modim out loud. The congregation recites their part silently but the leader does not.
And of course, you are leading prayers for the whole congregation before G-d. Ensure you keep a reasonable level of K'vana, i.e. you at least keep in mind that you are praying and ideally for each b'racha, understand the general message of it even if you don't understand every word. e.g. when you recite Barech Aleinu, you are asking for a blessing on the land, i.e. a good crop. There are Siddurim that have a small "heading" before each one and whilst you are breathing as they recite Amen, also read this to prepare yourself what you are about to pray for.
