As far as Universal Priesthood goes, there really aren't many structured rules and therefore churches and denominations that believe in Universal Priesthood are free to structure their hierarchy and perform the Eucharist however they wish.
Since the only principle it focuses on is that God is just as accessible to a new believer as He is to a pastor, elder, deacon, or whatever, the hierarchy isn't considered all that important.
The sacraments, preaching, and any other aspects of worship services can be performed however the church or denomination deems appropriate. That isn't to say that the Bible doesn't address these things at all, just that the doctrine of Universal Priesthood doesn't really address it.
Acts, Titus, and 1 Timothy, for example, talk about church leadership and and those that adhere to the 5 Solae will do their best to structure their hierarchy to fit those commands. Since the Bible itself spends a lot more time talking about the character of a good leader than it does about the hierarchy itself, you'll see a lot of churches structure themselves differently and generally maintain the belief that they have the freedom to incorporate some cultural customs like holding elections for elders and allowing congregants to vote on how to spend money rather than it being decided by elders or denominational leaders.
For the Eucharist, you'll usually see the Senior Pastor lead and an Associate Pastor assist. But even this varies pretty wildly. Many churches only have 1 pastor so they'll handle it by themselves or an elder or designated helper will assist. Many churches don't require the congregants to get up to receive the elements so ushers or other volunteers will pass the elements from pew to pew. If a pastor is out of town, in the hospital, or otherwise unavailable to lead, someone else will step in. And that person who steps in doesn't necessarily need any special training or ordination. I've even stepped in once at my church. I was notified a few days in advance that the Senior Pastor would be out of town and so I assisted the Associate Pastor. He led and I prayed over the elements. All that seems to be required in most cases is that you're in good standing with the church, you display a reverence for the process and you have an understanding of how the church handles things so you don't mess something up or do things out of order. I've also seen the elements passed at less formal services at youth camps where camp staff and counselors would lead.
You will also see the other end of the spectrum where there are denominations with very strict denominational hierarchies more comparable to what you see in Catholicism. I, personally, am less familiar with them but I believe you're more likely to find them in Lutheran and Presbyterian denominations than say Baptists or Pentecostal denominations.