Question: I am a GIS Analyst with one years experience and no idea where to begin with professional development. I'm competent with the ArcGIS platform, but I am not too familiar with its administration processes. I can work with basic Python programming. I'm taking a course in SQL next week, and I'm pretty terrible with web services.

Where/How/What should i focus on learning to step up to the next level in a GIS career.

Answer: 
You've really kind of answered your own question here, but I'll elaborate for the purposes of canonism. I'll provide you with some ideas based off of specific skills that I often see requested at the [GIS jobs clearinghouse](http://gjc.org). You can pretty much go two separate routes here (or both simultaneously) and both are pretty wide open:

**Building your analysis skills**
---------------------------------

* Learn about rasters. Zonal statistics, DEM/DSM's, viewshed analysis, local statistics, hydrologic modeling are all branches of [Geostatistics](http://en.wikipedia.org/wiki/Geostatistics), knowledge of which is important for analysis. The [Geospatial Data Abstraction Library](http://www.gdal.org) is a great repository for useful tools and information.
* Learn about remote sensing. I see plenty of job postings asking for expertise in analyzing and managing LiDAR datasets.
* Become familiar with geocoding, pretty much any entity that keeps address data is usually interested in utilizing geocoding.

**Building your GIS Developer skills**
--------------------------------------

* Python, Python, Python. You'll hear it over and over again here. This is **the** GIS scripting language. I used the free courseware from [Udacity](https://www.udacity.com/course/cs101) to learn Python, which I think they do a pretty good job of, but I suggest instead [Learn Python the Hard Way](http://learnpythonthehardway.org/).
* If you want to stick to the ESRI suite, learn **C#**. At the very least, Microsoft is sticking with this as its go-to language for a very long time. It's future is more certain than the .NET alternative, **VB.NET**.
* Learn SQL. For the most part, basic SQL is standardized across all major RDBMS platforms, with all the extra bells and whistles integrated into the special SQL languages such as T-SQL and PL/SQL. Don't bother with all that yet, if you get the basic standardized language down, you'll cover 80% of the things you need to do with it and the other 20% you can pick up as you need. [W3C](http://www.w3schools.com/sql/) has some great simple and straightforward samples to get you started here.
* Learn database architecture. Understand the concepts of normalization and relationships, what primary and foreign keys are, and how to build a database. There are a lot of jobs that involve structuring your GIS data. In the same vein, understanding the underlying structure of geodatabases is key if you want to become a developer in the ESRI suite of products.
* Learn web development. More importantly, learn Javascript. This is a rapidly growing field. I see tons of job postings from businesses that want web GIS applications. There are a few different API's you can familiarize yourself with. If you want to go open source, two popular ones are [OpenLayers](http://openlayers.org/) and [leaflet.js](http://leafletjs.com/). If you want to stick with ESRI, [I wouldn't go with Flash or Silverlight API's](https://gis.stackexchange.com/questions/6763/arcgis-web-apis-what-are-the-differences), I would use Javascript and HTML only.
I honestly believe that GIS is a fast growing and limitless field. Conor has answered pretty much most of what I would say. I think a programming/scripting/database/analysis background will get you far. 

But, ask yourself what it is that you want to be doing. Is there a field that interests you other than GIS? So many agencies are new at GIS and with Google Maps and Earth at everyone's fingertips, many more are ready to enter into the GIS world. Waterways, park services, environmental protection, utilities, streets, universities, hospitals, military, real estate, community planning, etc. are all using GIS technologies. Finding a niche that is both exciting and stimulating to you is a possibility with GIS.