Welcome to the forum. It’s good to hear of your interest in the Catholic Church. I myself converted from Lutheranism two years ago, so I know something of what you’re going through.
You can go to Catholic Mass (service), but as a non-Catholic you cannot receive Holy Communion. You are welcome to go up in the Communion line, though. When you get to the priest just put your right hand on your left shoulder, and the priest will give you a blessing.
About becoming Catholic, you’ll have to talk to the Catholic parish priest. It’s a process (sometimes referred to as RCIA, Rite of Christian Initiation in Adults), and usually takes at least a year. You can, under normal circumstances, not receive Holy Communion or sacramental confession before completing RCIA.
On a side note, as a Lutheran you in all likelyhood are already validly baptised and won’t need that again.