Here are a few things that I have learnt over the past few years of attending Taraweeh prayers, māshā'Allāh:
Tip number one: Do not fill your belly to bursting point at iftaar time! I'm sure you've heard that many times already, but it's worth repeating; it's that important to remember. If the masjid is too warm, you'll get sleepy during Qiyam. If you go for all 20 rakaat, you'll likely get a stitch! Would you eat a full meal an hour before swimming? The same logic applies here.
Tip number two: Try to avoid spicy/smelly foods at iftaar time. Instead, indulge your chilli and garlic tastebuds when you return home. Even if you brush your teeth real well before leaving for the masjid, your breath will still smell of digesting curry, and it's simply not good manners to inflict others with that kinda hardship! Especially when they're trying to worship Allāh in peace.
Tip number three: Don't sit or lie down after Iftaar. Get ready to leave for the mosque straight away, as otherwise you'll just get lazier, and more tired as the seconds tick by. Also, leave the dishes and cleaning until you return home, because it's just a waste of your precious time at that moment, and it will make you late to get that good spot in the front row!
Tip number four: Take someone with you to the mosque. Having company on your journey has many benefits: one, there is safety in numbers (especially important for sisters travelling late at night); second, if you're car-pooling, you'll get the reward of helping fellow Muslims in their worship (and of course, saving the environment); third, it may give you, or your companion, greater encouragement to fulfil the Sunnah of attending the Taraweeh prayers. Basically, it's all good, inshā'Allāh!
Tip number five: Read an English translation of the Qur'an, bit by bit, every day. I, personally, do not know very much Arabic; just a few words that are oft-repeated in the Qur'an. Therefore, I tend to easily lose concentration during the recitation, and more importantly, I do not fully appreciate the wisdom, warnings, and lessons that are being shared with me through Allāh's words. IMO, that's like, 70% of the value of Taraweeh lost, right there! Therefore, this year I decided to take a few minutes out in my day to read the English translation of the part of the Qur'an that I predict the imām will recite the same evening. I've asked around, and most imams usually get through a Juz n' a bit per night, in their aim to complete the Qur'an by the 27th night.
So with this new plan in mind, for the first four nights of Ramadan, I simply read the translation, and went to the mosque empty-handed, and waited for random familiar words to jog my memory. Alḥamdulillāh, it worked around 50% of the time, and my concentration improved greatly as I intensely listened out for my 'cues'. However, there were still chunks of recitation where my face was all screwed up in confusion, as I had little idea of what was being said. On the fifth night, I decided to take the translation with me, so I could read short passages during the breaks in between each prayer unit. Alḥamdulillāh, this drastically improved my rate of recall, and I felt I had a good idea of what was being recited about 90% of the time! Though, admittedly, it does depend on the speed of the reciter.
For best results, calmly read the entire portion that you think will be recited (or as much as you can) before arriving at the mosque. Then, during the rest breaks, speed-read through the few paragraphs that you predict will be recited in the following two rakat.
Of course, if you're 'in' with the imām, you could simply ask him for the exact bits of the Qur'an that he will be covering each night – I don't have that luxury, hence all the 'predictions'. :)
If you're already blessed with a working knowledge of Arabic, māshā'Allāh, then try to read the tafseer regularly instead, for a deeper appreciation of the recitation.
Tip number six: Save up some du‘ā’. Depending on how many rakat your mosque completes per night, you will have multiple opportunities to make du‘ā’ during the blessed moments of sujood. Pick a few 'faves' and try to fit them in when you can.
Tip number seven: A special one for the laydeez. If you're not in a state to pray Taraweeh due to menses or nifaas (post-childbirth bleeding), you can still benefit from the community spirit of worship, by sitting in a place away from the masallah (i.e., the place where people make sujood), with a copy of the English-Arabic Qur'an, and silently follow the imām as he recites. Make sure not to touch the words of Allāh directly in an impure state – wear gloves, or use some other clean barrier to touch the pages.
Disclaimer: I am aware of differences of opinion in this matter, so please consult with your imām or other local knowledgeable person if you're not sure. If you don't wish to attend the masjid, then you can always watch an online transmission of the Taraweeh from masjid-al-Haram in Mecca Mukarramah.
I haven't been attending Taraweeh for very long, but I aim to make it my own Ramadan tradition, inshā'Allāh. Employing such small tips helps make the experience more productive and enjoyable. I invite the more seasoned Taraweeh-goers to add your own tips below, for the benefit of all. JazakumAllah khair in advance!