At my first HHD services I was not yet a Jew. After the first year I learned to wear more comfortable shoes and taper off on coffee AHEAD of the fast.
My go-to book for preparing for holidays that were new to me was "The Jewish Holidays: A Guide and Commentary," by Michael Strassfeld. It is easy to read and has each holiday in a separate chapter. It covers all the practical stuff like - what to do when somebody greets you on the high holy days with a phrase you've never heard before and what to say back. (Ya gotta know more than just Shabbat Shalom this time of year or you'll be tongue-tied when approached.)
I was surprised the first year by the extra choreography some of the men engaged in during the service. I guess they were raised Orthodox, perhaps? I knew to go up on my toes three times when the words Kadosh, kadosh, kadosh were said, and I had the bowing down from practice during regular services, but there was a lot of swaying and other movements that I hadn't seen before.
I was also very surprised how much yacking went on in the pews among the congregants during the service. It was like old home week for people who didn't see each other for a long time - maybe only once a year or less. Services got off to a late start to accommodate the schmoozing.
At the Break the Fast I was surprised by how people didn't run to the food table at first. They mobbed the soda table gulping down large glasses of it.
If you're going to spend all day at services and do the whole thing - Selilchot, Erev Rosh Hashanah, Two days of Rosh Hashanah, Kol Nidrei, Yom Kippur (morning, afternoon, Yizkor and concluding services), I recommend really doing some thinking about what you are going to pack in your purse/car ahead of time to make yourself more comfortable. It can feel like a marathon if you don't bring along some things you might need when away from home. Think of it like spending a whole day and evening as a tourist in an unfamiliar city. What would you bring along?
Change of shoes
Snack (obviously not for Yom Kippur)
Cell phone and charger (keep in the car)
Favorite toy/comfort object for your child
Small hand fan
My best advice for first-timers is, don't be hard on yourself if you feel overwhelmed. Even after a couple decades it is an overwhelming experience for me some years. Emotions run high, people feel crowded in a confined space, parking can sometimes be a challenge, relatives who may have "issues" find themselves in close proximity to one another and services are long and you get hungry, you can't always control the temperature or who sits in front of you or next to you or behind you. If you have children you are responsible for thinking about what you can realistically manage with them. You may want to "do it all", but you may be better off picking and choosing only some services to attend. If you have children and a partner, negotiate ahead of time your responsibilities at services with the children. Who leaves with the child if they start fussing, for instance. If you are a single parent, see if you can find another adult to help relieve you if you need a break. Don't wait to find someone when you walk in the door; find another parent to trade off with or something ahead of time.
Expect to cry. You might. The music and mood can sweep you away. The sound of the shofar, the chanting of Kol Nidrei, the words read and said all elevate the service beyond the norm.
If you have a reluctant partner who doesn't want to "do it all" with you, let go of your expectations of being together through each and every service. Newbies are enthusiastic and want to make sure they experience it all, while those not as plugged in or who are veterans may find your enthusiasm grating and take your excitement about going to every service and staying until the very last minute of it as nagging. (I start negotiating with my spouse about attendance a month ahead and we write it on the calendar - which ones they will attend and which ones not - so everybody knows what the other is willing to do.)
The fact that time must be taken from work always becomes an issue with somebody in the family, and as a Jew by Choice I can sometimes get my hackles up when they balk at taking a particular day off and missing a service.
Over the years I have learned I have to let it go. I can only be responsible for my own attendance and cannot control the rest of my family.
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I wasn't a Jew at the time I attended my first Rosh Hashanah service, but was studying to convert. I was very confused. I was told they'd be very different, and, boy, they sure were. But, oh, the music! So compelling. Since then I've taken some classes, which I highly recommend. And I know the themes now. The music is still as haunting as ever. And there's nothing like stepping into a grand hall filled with a thousand Jews. Some are your friends, and some you only see once a year.
* * *
Last year I experienced the High Holy Days for the first time, as someone going through conversion, but not yet a Jew. I happened to be dating someone at the time that, while Jewish, is not as observant as I am (or was at that time, even). So, I made a lot of compromises about what services I would attend, and how much time I would devote to observing the season, and I wish I'd managed that differently. I guess my advice would be, "Decide for yourself how much you want to participate in High Holy Days observances, and don't be swayed by the feelings of other people." The really wonderful thing that I did for myself last year, though, was to take a "Hebrew In a Day" class with Lehrhaus the week before the High Holy Days. The services (and the conservative machzor) are very Hebrew-oriented, and it increased my comprehension dramatically.