In Texas you are assessed on 100% market value of your property. Depending on where you live, you are taxed by several different entities starting with the school district and going so far as special water and fire districts. Your assessed value will be based on what the value of the property was on January 1st of the taxing year. So, right now we are working on the 2006 tax year and values are based on 1/1/06.
You will receive a Notice of Appraised value in the summer after May 1. Not all are sent on May 1 as they have to send several batches out due to the sheer volume. If you do not agree with the Appraised Value, you have 30 days from the mailing of the Notice to Protest. When you protest you will be required to show evidence as to why you think your property has been over-valued for the current tax year.
Once a majority (somewhere over 90%) of the property values have been resolved, the appraisal district can then "certify" the tax role. That's when the taxing entities get rolling on a tax rate. The total tax you pay, like I mentioned before, is a sum of the taxes from all entities that have jurisdiction.
In the fall you will receive a tax bill based on the finalized value (might be different than the Notice value if you protested and were successful in getting it lowered). This bill will be due by Jan 31 of the next year, in our case 1/31/07. If you have a mortgage, the mortgage co. will receive and pay the bill. If you are short in escrow, then comes the trouble especially for those ignorant to the "system". That's when the mortgage company jacks up your payments to make up for the shortfall as well as to get enough balance for the next tax year.
If you were living in the house January 1, 2006 and you don't have a Homestead Exemption anywhere else in Texas, please be sure to file an application for Homestead ASAP! This exemption will protect you from any year to year increase over 10%. I.e. the appraised value may rise 12%, but your taxable value will only rise the 10%. (Unless you add any new construction to the property, which there's no protection from)
Travis Central Appraisal District has a pdf file of LAST YEAR's tax rates, the new tax rates have not yet been determined. You can search the appraisal role for your property to be sure which entities are taxing you (should be listed on the detail). These entities are political in nature so the chances of absurd tax increases are slim.