I spent about 20 years of my life as a United Methodist, I'm the daughter of life-long Methodists, and the grandaughter of a Methodist minister. I'm now an LCMS Lutheran.
Here's my take on a few of the differences:
Theology: There is a huge difference between Luther's "Theology of the Cross" and Wesley's theology of "Entire Sanctification." The differences are too long to get into here, but I would suggest googling them and seeing what you come up with.
Communion: Others have already covered the theological differences well (the main difference being that Methodists believe that Christ is present "only after a heavenly and spiritual manner," while Lutherans believe that Christ's body and blood are given to us to eat and drink in, with, and under the bread and wine.) I'll just add that Methodists practice open communion, and the LCMS does not. My last Methodist church communed two practicing Muslims whenever they would visit as Islamic goodwill ambassadors. Some LCMS congregations (including mine) allow other Christians to commune if they agree with certain key doctrines, while others won't allow anyone outside of their own congregation to commune. The most common approach is churches communing all other LCMS members. Methodists are fond of saying "It's the Lord's table, not a Methodist table" LCMS Lutherans believe it is the Lord's table, but also believe that the Scriptures teach that people who commune not properly discerning the Lord's body and blood do themselves great harm, and so feel a responsibility to guard against this. Methodists use grape juice. Lutherans use wine. Methodists often use leavened bread. All Lutherans I've ever seen use unleavened bread. I have often seen where the words of institution are not used in their entirety in Methodist churches. In my experience, they are always used in their entirety in the LCMS. This is because we believe it is the Word of God that makes a sacrament a sacrament. In my experience, Methodist churches have communion about once a month. Most LCMS churches have communion every other week. Some have it weekly.
Baptism: LCMS Lutherans believe that through the Word of Christ in and with the water of baptism God cleanses us from original sin, imparts faith, fills with the Holy Spirit, makes one a part of the church, and gives forgiveness of sins. This is 100% the work of God and not of man. Whether or not the regenerate person retains the salvation they are freely given depends on whether or not they continue in repentance and faith. I'll let the Methodists give you their view of baptism, since I've always been a little unclear on it.
Authority: Lutherans believe the Scriptures alone are the sole rule of faith. Methodists believe matters of faith are guided by the Wesleyan Quadrilateral: Scripture, Traditional, Reason, and Experience.
Confession and Absolution: Methodists have a form of this that you will hear from time to time, but in my experience, it's not used often in the liturgy. In the Methodist version I'm familiar with, the Pastor will absolve the congregation, and the congregation will turn around and absolve the Pastor. Lutherans practice corporate confession and absolution every week. Lutherans believe that the Pastor has authority from God to forgive or retain sins in Christ's stead and by His command. I'm not really sure what the Methodist view of this is. In my personal experience, I don't ever recall hearing it expounded on.
Pastors: Methodists ordain women. LCMS churches do not.
Social Issues and Morals: The Methodist church is a HUGE tent. You will find an incredible range of both theological and moral beliefs in the Methodist Church -- everything from extremely liberal to extremely conservative, and everything in between. LCMS tends to be very conservative.
Liturgy: Methodist liturgy tends to be (but is not always) less formal and can vary a great deal from place to place. Lutheran liturgy tends to be (but is not always) more formal and varies a bit less.
Miscellaneous: Methodist Pastors generally wear black robes. Lutheran Pastors generally wear white ones. Methodist choirs are usually at the front of the church. Lutheran choirs are generally at the back. Methodist hymns deal a lot with inspiration and christian living. Lutheran hymns deal a lot with the cross and theology. Lutheran hymns can be challenging to sing if you're not used to them.
Confirmation: I was confirmed as a child in the Methodist church. There were a few classes beforehand -- not long, and a big deal wasn't made out of it. GraceSeeker is right that Lutherans put a lot of effort into confirmation - unfortunately, not all of which pays off as far as kids staying in the faith. The kids in my church do confirmation with the Pastor for two years. In that time, they memorize 60 scripture verses and Luther's shorter catechism in its entirety. It's a big deal.
Governance: Methodist churches have bishops. Lutheran churches in the US don't. The local congregation is autonomous in the LCMS.
Creeds: Methodists use lots of different creeds and affirmations. Some of the affirmations, in particular, I have found troubling. When I was growing up, the Apostle's Creed was used most of the time in the Methodist Church. As an adult, it seemed like Korean Methodist creed was getting a lot of use. Lutherans use three: the Apostle's, the Nicene, and the Athansian.
Confessions: Methodists have a set of doctrines, but there is wide latitude about what individuals can believe. LCMS Lutherans have the Lutheran Confessions, and it is pretty much expected that you will adhere to them. Lutherans place a GREAT DEAL of emphasis on the content of what we believe, and the LCMS approach to finding a church is generally focused on finding one that teaches doctrine accurately. Agreement on doctrine is not as much of a central issue for Methodists as it is for confessional Lutherans.
Alcohol: As others mentioned, Lutherans generally don't have any problem with drinking alcohol. Some Methodists do, and some do not.
Sermons: In my experience, the overwhelming majority of Lutheran sermons I have heard are focused on the cross in one way or another. The overwhelming majority of Methodist sermons I heard in my 20 years of being a Methodist dealt with Christian living.
Well, that's just a few thing I can think of off the top of my head. Some are important issues, others just random bits of info. Hope it helps, and please feel free to correct me, anyone, if I've misrepresented Methodism in any way.